Answers to odd-numbered exercises1 - University of...

Answers to Odd-Numbered Exercises Burda/Wyplosz Macroeconomics: A European Text Chapter 2

Answers to odd-numbered exercises1

Chapter 2 1. National accounts

• NDP = GDP – depreciation = 5000 – 500 = 4500

• National income = NDP – indirect taxes + subsidies to enterprises = 4500 – 1000 + 400 = 3900

• Personal income = National income

- social security contributions - net corporate saving - corporate taxes + transfers to households

= 3900 – 700 – 600 – 100 + 600 = 3100 since transfers to households = transfers to households and enterprises – subsidies to enterprises = 1000 -400

• Personal disposable income = Personal income – personal taxes – fines and fees = 3100 – 1500 – 100 = 1500

• Consumption = Personal disposable income – household savings

= 1500 – 200 = 1300

• Government purchases = Consolidated government deficit + taxes – transfers = 100 + (100 + 1500 + 700 + 1000 + 100) - 1000 = 2500

• Current account balance = GDP – absorption = GDP – (C + I + G) = 5000 – 1300 – 1200 – 2500 = 0 3. Wrong. Services are value added and contributes to GDP exactly as industrial value added. 5. (a) Nominal GDP is:

• In 1993 GDP93 = 300 + 200 + 250 = 750 • In 1994 GDP94 = 400 + 450 + 240 = 1090

Real GDP in 1994 is measured using 1993 prices: 1 Many thanks to Michael Kvasnicka for a thorough proofreading of these solutions. -MB & CW.

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GDPr94 = 400 + 300 + 200 = 900 GDP deflator inflation = (1090-900)/900 = 21.1%. (Note that the approximation given by the difference between nominal and real GDP growth is poor in this situation; better to calculate the GDP deflator directly and use it to compute the inflation rate). (b) Set the CPI at 1.0 for 1993. It corresponds to a basket of 300 apples, 100 pears and 50 units of petrol which costs 750. The same basket would cost 900 in 1994. Then the CPI in 1994 is 900/750 = 1.20. CPI inflation is 20%. 7. The solutions are as follows (subject to interpretation!)

• deficit in merchandise trade account • deficit in the long-term financial account (if a house is considered as a long-term

investment) • no effect • deficit in the invisible balance (paying for work) • surplus in unilateral transfers • surplus in short-term financial account • deficit in unilateral transfers • deficit in invisible balance (net investment income) • surplus in long-term financial account (direct investment) • surplus in official intervention accounts (not in Euroland anymore!) • deficit in errors and omissions

9. Officially recorded drug business would indeed show up in the GDP for the local value added (importer’s income, refining and distribution income). Tax receipts would increase accordingly. But if people consume more drugs, become addicted and are less productive, the GDP might decline, and tax receipts too! There would be no overall effect on the balance of payments. Previously legally imported material was recorded as errors and omissions, now it will show up instead in the trade account.

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Chapter 3 3. (a) We know that at the steady state s y = δ k, so s = δ (k/y) = δ (K/Y) since y = Y/L and k = K/L. So we need: s = 0.05 x 2 = 0.1, i.e. 10%. (b) We know that at the steady state s y = (δ + n + a) k, so s = (δ + n + a)(k/y) = (δ + n + a) (K/Y). We also know that output and capital grow at the rate a + n. So a + n = 0.03 and we need: s = (0.05 + 0.03) x 2 = 0.16, i.e. 16%. 5. If capital and labour inputs double, output is YKLKLLK 224)2)(2( ====Y , so it doubles too. We have constant returns to scale. The marginal productivity of capital is

KLKY // 21=∂∂ and the marginal productivity of labour is LKLY // 2

1=∂∂ . Both decrease when the corresponding input increases. 7. The production function is Y = F(K, AL). So as A grows, we are able to produce more with the same capital stock, or the same amount with a smaller capital stock. Technological progress thus allows us to invest less while producing more. Less investment means less saving, therefore more consumption. Intuitively, at a higher rate of technological progress, maintaining the same steady state output and capital stock per efficiency unit of labour yields too little consumption, so optimal capital stock per efficiency unit will be lower. 9. The result is explained in Figure S3.9 (assuming on-going exogenous technological change): Y/L I/K

t t Figure S3.9

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Chapter 4 1. The figure below shows that the household’s budget line shifts upward by the amount of the inheritance B. Under plausible behavioural assumptions (both leisure and consumption are “normal,” the optimum choice moves from R to R’: both consumption and leisure increase. It is conceivable that for B large enough (not shown, another good exercise to try), the

household may even decide not to work at all (i.e. this is called a “corner solution”): if you were born to a very rich family, you might do the same!

−= ll

Consumption R2 R1 B

l leisure −

Figure S4.1 3. Easy, but a devious question! If the minimum wage is lower than the equilibrium wage, it has no effect. 5. The graphical derivation of the collective labour supply curve is shown in Fig. 4.11 in the textbook. What is interesting is how the shape of the indifference curve affects the shape of the collective labour supply curve. Below, we look at two sharply differentiated cases. (a) In Figure S4.9(a), the trade union that represents the workers is “hard-line”. Its indifference curve is very flat to show that it cares a lot about the real wage and little about employment. The collective labour supply schedule is very flat, quite distinct from the individual supply schedule (Fig.4.12 for example) (b) Figure S4.9(b) looks at a “job-first” trade union which cares relatively little about the real wage and aims at a level of employment: its indifference curve is quite steep. The implied collective labour supply schedule is nearly vertical, not unlike that of the individual supply schedule.

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Real wage Real wage Collective supply

Collective supply

Employment Employment

Figure S4.5(a) Figure S4.5(b) (c) When the trade union reacts asymmetrically depending on whether labour demand is rising or decreasing is a combination of (a) and (b): the labour supply schedule is steep when labour demand is rising (it fights for higher wages) and flat when it is declining (it fights to keep the real wage unchanged ). 7. Labour taxes increase the cost of labour to employers for a given take-home wage. The result is that labour demand is lower, the higher is the tax rate, and therefore the lower is employment.2 When unemployment benefits are paid for by labour taxes, the higher is unemployment, the higher must be the tax rate applied to labour and therefore the higher is the real cost of labour. An increase in unemployment thus raises labour costs and reduces employment, creating further unemployment. A really vicious, but not uncommon, circle! On the other hand, linking the tax rate to previous layoff history of individual employers (“experience rating” as done in the United States) reduces employers’ tendency to lay off workers. 9. (a) The increase in labour supply is shown in Figure S4.9 below, patterned after Figure 4.8 in the text. The result is an increase in equilibrium employment (more females work) and a fall in the equilibrium real wage. Some male workers may be upset enough to quit working, making room for more female workers, thus raising voluntary unemployment. If the real wage is rigid and above the equilibrium wage as in Figure 4.12, there is more involuntary unemployment. Does the entry of women create unemployment, then? Yes and no.

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2 Formally, the demand curve for labour corresponds to the equality of marginal productivity of labour and real labour cost, c: MPL(L) = c. The real cost of labour is c = (1+t)w, where w is the real wage and t is the tax rate on labour. So the higher is t, the higher must be MPL, and since MPL is a declining function of L, L declines when t rises.


mechanically yes, but the true cause of unemployment is wage rigidity, not the entry of women into the labour force, as Figure S4.9(a) illustrates. (b) As explained in Chapter 6, if the marginal productivity of capital, more capital will be put in place, which will raise the demand for labour, as shown in Figure S4.9(b) below. Not only does employment rise even more, but the equilibrium wage is now higher than in case (a) (it may be that the equilibrium wage does not decline at all, or even increases). Who said that women make men miserable? Real wage Real wage

supply supply

A C

A B

B

demand demand

Employment Employment

Figure S4.9 (a) Figure S4.9 (b)

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Chapter 5 1. If 10% of the coconuts deteriorate, the real interest rate is –10%: one coconut saved today earns 0.9 coconuts tomorrow, hence the slope of the budget constraint. Since Crusoe cannot borrow, the budget line is truncated at his endowment point A (he cannot consume today more than today’s endowment). Consumption tomorrow Y2+0.9Y1 Y2 A Y1 Consumption today 3. (Typo in book: the reference should be to Figure 5.8 in the textbook!) If there is an initial debt D0 (value in period 1), the budget constraint becomes: D0 + (G1 –T1) + (G2 –T2)/(1+r) = 0, which can be represented in the following way, which is slightly different from Figure 5.8: Budget balance tomorrow -D0 0 Budget balance today -(1+r)D0 5. The net present value of the firm is the discounted sum of all expected future payments, i.e. dividends plus resale value, less the initial investment.

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- With no resale value, it is:

412,21€)10.1(

000,56)10.1(

000,5210.1000,40000,100 32 =+++−=V

- With a resale value of €20,000 in the last year:

438,36€)10.1(

000,20)10.1(

000,56)10.1(

000,5210.1000,40000,100 332 =++++−=V

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Chapter 6 1. First period income Y1 is unchanged, while expected income in period 2 increases from Y2 to Y2’. Consumption rises in both periods as the household borrows now against future income to raise consumption in period 1 as well. This is called consumption smoothing. Consumption tomorrow Y2’

A’ Y2 A Y1 Consumption today 3. A primary motivation to save is to put aside income for retirement and the subsequent income decline which results (Y1 is large relative to Y2). Health conditions in poor countries are often deficient, an the result is shorter life expectancy. As people die earlier, there is less saving and the average age of the population is lower. 5. When a country cannot borrow abroad it cannot bring forward future income, so consumption is lower than otherwise. Similarly firms cannot borrow to finance productive investment, which hurts growth. An increase in interest rates on the other hand for countries already cut off will, almost by definition, be irrelevant. 7. (a) Figure S6.7(a) shows the graphical solution. The initial position is described by the endowment at point R and the chosen consumption pattern at point A. (i) A temporary increase in income moves the endowment point to R’ and optimal consumption is shown as point A’. The household is now a net lender, which makes sense: some of the windfall gain is saved for later, when income will revert back to the lower level. (Note that the fact that the household becomes a net lender is not necessary; there might just be less borrowing.) (ii) The permanent increase is shown as the new endowment point R” and optimal consumption point

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A”. With income rising in both periods by the same amount, the household has no reason to change beyond spending more in both periods: the net borrower remains a net borrower. (b) The case of a net lender is shown in Figure S6.7(b). A temporary increase in income means even more net lending in period 1. A permanent increase does not change the general pattern, as was the case of the net borrower in (a): the household spends more in both periods and remains a net lender. Consumption tomorrow Consumption tomorrow

A”

A” R” A’ R”

A’ A

R’ R R’ R A

Consumption today Consumption today

Figure S6.7 (a). Net Borrower Figure S6.7 (b). Net Lender

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Chapter 7 1. The value of the exercise is in making you think about the fact that there is no unambiguous answer. Here are our answers, but feel free to argue why you disagree!

(a) traded, if we consider foreign tourists eating in our restaurants. (b) traded once we are free to bank in any country, but nontraded in practice.

(c) mostly nontraded, except for prestige buildings which attract architects from all over the world. (d) mostly nontraded; who reads foreign newspapers? (e) traded within Europe, unless the mad cows are rampant! (f) nontraded, except maybe in border areas.

3. If the country operates inside the PPF, say at point P in Figure S7.3(a), its spending is lower than if it were operating anywhere in the hatched area, meaning that it foregoes the ability to achieve a higher level of utility. Next, suppose that the economy operates at point P in Figure S7.3(b) which is not at the tangency with the price line whose slope is -σ. By reallocating production towards point P’, producing more nontraded goods and less traded goods, it is possible to reach a higher budget line, hence a higher indifference curve. (Technically, at point P, the marginal rate of transformation, given by the slope of the PPF at point P, is less than the relative price σ.) Traded Goods Traded Goods

Budget line

P

P’

P -σ

Nontraded goods Nontraded goods

Figure 7.3(a) Figure 7.3(b)

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5. Figure 7.5(a) shows the case of a trade surplus. Production takes place at point P, consumption at point C. The distance PC represents the surplus. Note that consumption and production of nontraded goods must be identical (why?). Also note that the consumption point is below the budget line that corresponds to production: a country that runs a current account surplus is actually saving. Figure 7.5(b) shows the opposite case of a trade deficit, in which a country is “living beyond its means” in the sense given by its present production. Of course, a country with access to credit markets, a windfall grant, or with a stock of foreign assets can do precisely this. Traded goods Traded goods

C

P P

C

Nontraded goods Nontraded goods

Figure S7.5(a) Figure (b) 7. See Figure 7.8: the real exchange rate should appreciate. 9. See Figure 7.8. An increase in the interest rate effectively increases the debt burden and forces the country to achieve a higher primary current account surplus. This will frequently require a real exchange rate depreciation.

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Chapter 8 1. If you send your answer (and it is correct), it will be posted on the website for the benefit of your fellow country persons. 3. Daphne brings 1000 rupees in cash to her Eurobank. It turns out to be worth €600 at today’s exchange rate. (a) the bank credits Daphne’s account and keeps the rupees

Assets Liabilities

Foreign currency vault cash Daphne’s account + R 1000 + € 600

(b) The Eurobank sells its rupees to the European Central Bank:

Eurobank ECB Assets Liabilities Assets Liabilities Reserves Daphne’s account Foreign exchange Eurobank + € 600 + € 600 reserves + R 1000 + € 600 5. M1 is defined as the sum of bank notes in circulation and deposits of the private sector in banks (excluding the public sector’s deposits). So we need to find out the amount of bank notes in circulation and the public sector’s deposits. We know that the consolidated gross debt of the consolidated public and private sectors is the sum of their net debt and their bank deposits: Gross debt of the consolidated public and private sectors = 1000 + 1600 = 2600 The amount of bank notes in circulation appears in the consolidated balance sheet of the public and private sectors, see Figure 8.1, which implies that: Bank notes + Deposits of the Private Sector + Deposits of Government + Private real assets = Government and Private Gross Debt + Net Worth

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So: Bank notes = Public and Private Gross Debt + Net Worth - Deposits of the private sector - Deposits of Government - Private real assets = 2600 + 400 – 2000 – 600 = 400. Finally: M1 = 400 + 2000 – 200 = 2200. 7. (a) The credit available represents money available for immediate spending – quite like bank lending – and is readily accepted. (b) Utilized credit is money already drawn and in effective use. (c) What is accepted by the vendor is money on the bank account of the customer using the credit card, which is transferred into the account of the vendor. This amount is thus already accounted for in the definition of money. 9. Velocity is defined in the text in equation (8.2) as: V = Y/L(Y, i, c)

(a) A temporary increase in inflation will not affect the nominal interest rate – recall the Fisher principle, thus leaving velocity unchanged.

(b) A permanent increase in inflation raises the nominal interest rate by the same amount. This reduces the demand for money and therefore raises velocity.

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Chapter 9 1. The money market is chiefly an interbank market. When a bank wants to lend its excess reserves, it can either find a counterpart in the market interested in borrowing, or deposit them with the central bank. Since the latter is always possible, it would make little sense to lend at a lower rate. Conversely, a commercial bank which wants to borrow reserves can always get them from the central bank at the lending rate, and would never pay more. 3. When the central bank creates money, for example by lending to commercial banks, the cost is virtually nil but it acquires an asset (the commercial banks’ indebtedness) which carries an interest. When the commercial bank creates money by lending to its customers, the cost is also small (see next question) and it acquires an interest-yielding asset, its customers’ loans. Both actions increase the money supply. 5. Look at equation (9.9). It can be rewritten as P = mM0/L (.). If the multiplier m is constant, we find that inflation is π=(∆M0/M0)/(∆L/L). If money demand L is unstable, a low and stable growth of M0 will not deliver a low and stable rate of inflation. Targeting M0 will not work well. 7. Both appear in Figure 9.2. Bank reserves are in domestic currency, they are assets of commercial banks and liabilities of the central bank. Foreign exchange reserves are in foreign currency and are assets of the central bank. 9. Using the formula (9.8) in Box 9.1 we find that the multiplier is m = 1/0.2575 = 3.88. The central bank will want to increase M0 by €2.575 million. 11. a) The effects can be seen as follows:

Central Bank Commercial Banks Assets Liabilities Assets Liabilities Treasury Bills Foreign exchange +€ 50 m M0 + € 40 + € 10 m Foreign Exchange Reserves - € 10 m Treasury Bills

- € 50 m Bank Reserves + € 40 m b) With a required reserves ratio of 25% and assuming no currency holdings, we have a multiplier of 4, so the money supply should increase by 4x40 = € 160 m.

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Chapter 10 1. In Figure S10.1 below, each of the curves are defined as sets of output and interest rate pairs (Y,i) which establish equilibrium in either the goods (IS) or money (LM) market. Points along the IS curve are characterized by equality of aggregate demand and output/income, so all (Y,i) combinations above the IS curve can be thought of interest rates which are too high to generate enough demand given output; this is an excess supply of goods. Similarly, every point below the IS curve characterizes an excess demand for goods. By the same logic, it is clear that every point below the LM curve corresponds to an excess demand of money, while every point above corresponds to an excess supply. The IS and LM curves then define four quadrants in the figure below, each one corresponding to a disequilibrium situation in both markets: i Excess supply of goods and money LM excess demand for excess supply of goods goods and and demand for money supply of

money excess demand for IS

goods and money Y Figure S10.1 3. One way of thinking about an increase in productivity is an upward shift in the production function in panel (b) of Figure 10.6: more output can be produced using the same input of labour 3 Equilibrium output increases and the supply schedule in the IS-LM diagram (panel (c)) shifts to the right. In all likelihood, the increase in productivity will correspond to an increase in the marginal product of labour, shifting the labour demand curve in panel (a) to the right; wages will rise. Trickier is the issue of the real interest rate. It is likely that the marginal product of capital will have increased, increasing the interest rate in panel (c) consistent with equilibrium output; yet in general equilibrium it will be necessary to check the equivalent of Figure 10.7 to solve for the equilibrium interest rate which makes households content to save and consume in the first period as they do; in this case the IS will intersect the S curve at only a somewhat higher interest rate, say A´, which lies below the old LM curve. Increasing output leads to a rightward shift of the money demand schedule. Given prices at their initial level, the real money demand exceeds money supply. Given the nominal money supply, a higher real money stock is now necessary for the LM to intersect where IS and S cross. This is only possible if the price level falls, raising real money balances enough to induce a sufficient rightward shift in the LM curve.

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3 One could also think of a horizontal shift of the production function, leaving the marginal product of labor unchanged at given output. This would, however, imply positive output with zero inputs, which seems implausible.


When prices are sticky in the short run unemployment results, as aggregate demand for goods determines output; the production function generates “technical unemployment”. In terms of Figure 10.11, the economy will stay at the same level left of the new supply schedule and the money demand schedule does not shift. Due to the increase in productivity however, this output can now be produced with less labour. A more elaborate story might also allow for investment in capital which might shift the aggregate demand for goods and services outward in response to new profit opportunities. In this case there would also be further additional destruction of jobs as productivity increases. In both flexible and fixed price cases, an increase in productivity also increases wealth, so that consumption will tend to increase, additionally shifting IS to the right. Hence, in the first case the price level decreases by less, and in the second case employment decreases by less. 5. In Figure 10.6(a) labour demand and collective labour supply are equal at a wage (point A) at which not all labour supplied by households is employed by firms. This corresponds to a case of involuntary unemployment at real wage w, in the absence of nominal price rigidities. In the presence of this real wage rigidity, wages are above market-clearing level, and supply in the labour market exceeds demand. Labour demand determines the amount of labour used in production, which is less than the market-clearing employment level. Hence, output is lower, and the supply schedule in panel (c) is to the left of what it would be corresponding to the intersection of household labour supply and labour demand. Equilibrium in the money and goods markets will still be achieved via flexible prices, however. Excess demand in the goods market (point A) will lead to rising prices, a leftward shift in the real money supply in panels (e) and (f) and to a leftward shift of the LM function in panel (c). At the same time as output decreases, the money demand curve shifts to the left. Prices rise until the IS curve, the LM curve and the supply schedule intersect. In the end the economy is dichotomized, and money is neutral, since money cannot affect the real equilibrium, which is determined without reference to it. It is important to keep in mind that equilibrium in the labour market occurs with involuntary unemployment at the household level; with real wage rigidity, nominal wages rise by the same amount as prices do. 7. An increase in transaction costs shifts up real money demand and drives the LM schedule to the left. In goods markets this will yield an excess supply, and when prices are fully flexible this will simply lower the price level until the LM schedule has moved back to its original position. GDP, employment and the interest rate are unchanged. With sticky wages and prices as in Figure 10.11, output is determined by demand, and GDP falls below, and the interest rate will rise above its previous equilibrium level. This will produce involuntary unemployment likeL-L in Figure 10.11 in the textbook. Since both the nominal wage and prices are fixed, the real wage is also fixed.

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9. (a) Investment raises productivity shifting up the production function in panel (b). While this is likely to leave labour supply unchanged in the first instance, it will raise the marginal product of labour and thereby shift out the labour demand curve in panel (a). (b) Raising productivity the economy can increase output with a given amount of labour. This shifts the supply schedule in panel (c) to the right, creating excess supply in the goods market. In addition, increasing productivity raises wealth, and at least to a certain extent consumption, which shifts the IS schedule to the right. (c) Excess supply in goods markets will result in falling prices, shifting the LM schedule to the right, lowering the interest rate and raising demand until goods markets are in equilibrium. If the wealth effect is taken into account, prices will decrease by less, since the IS curve will have shifted to the right; the equilibrium will be characterized by higher interest rates than otherwise. (d) With sticky prices, goods markets remain in disequilibrium, so GDP (output and income) is determined by the level of aggregate demand, which is determined by the intersection of IS and LM curves. Employment determined by effective demand for labour. (e) In principle, the central bank could increase the money supply, shifting out the LM schedule until equilibrium is consistent with aggregate supply.

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Chapter 11 1. Consider the following diagram: Interest rate i LM FI

II

V

Figure S11.1 The six regionmoney and sh I: Excess demII: Excess supIII: Excess suIV: Excess suV: Excess demVI: Excess de

3.(a) The eaccommodatecurve shifts rioutput has inhas deteriorat (b) Capital odevaluation. However, whcurrency at ththe market reFrom the domrates: the finaB in Figure 1the interest ra (c) Two reasopublic sector The second re

VI

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III

V

d pi

s su d

s dsses

sone a

ixis ct inf

s Csta

ins ne

I

IS

Output Y

to the following six regime combinations for goods, tal markets:

supply of money, capital inflow pply of money, capital inflow emand for money, capital inflow emand for money, capital outflow

demand for money, capital outflow s supply of money, capital outflow

hifts the IS curve rightwards. As the government ey demand through increase in money supply, the LM new equilibrium similar to point C in Figure 11.14 where nd interest rates remain unchanged. The current account

ed exchange rate system indicates that agents fear a freely mobile, returns must be equal across countries.

ts a devaluation, agents are reluctant to buy domestic rate. They now face a higher opportunity cost. Therefore, al return on assets denominated in the weak currency.

view, this is equivalent to an increase in foreign interest hifts upwards and the economy will tend to move to point apital controls allows the government some control over y (for a while) at point A.

g. First, the opening up of a budget deficit meant that the being violated unless future corrective action was taken. xt chapter: with demand stimulated, prices were likely to

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rise and competitiveness to be eroded. Ultimately a depreciation would be required, prompting further price increases, requiring further depreciation, etc... 5. The decline in oil prices means an exogenous loss of income for Norway. It would also result in lower investment expenditures for the oil industry, a significant chunk of Norway’s economy. This is represented by a leftward shift of the IS curve, depicted in Figure S11.5 below. Norway fixes its exchange rate to a basket of currencies, so the fall in interest triggers a reduction in money supply until the LM curve passes through point C. The result is a recession. Two options are available : - An expansive real demand policy, shifting the IS curve back to its initial position. - A (surprise) devaluation which shifts simultaneously the IS and the LM curves to the right. Interest rate i LM A i* C B IS IS´ Output Y Figure S11.5 7. The LM curve is 2000 = 0.5Y - 300i. ForS = 1 andG =T = 3000, the IS curve is Y = 15500 - 500i . But in a fixed exchange rate regime i = i* = 10, so the equilibrium interest rate must also be 10; Y can be read straight off the IS curve: Y = 15500 - 5000 = 10500. The money supply is endogenous, since the central bank is committed to intervene an much as necessary to maintain S = 1. Using the demand for money function, we find L(Y, i, c) = 0.5(10500) - 300(10) + 500 = 5250-3000+500 = 2750, which at P=1 corresponds to a nominal money demand M=2750. Higher interest rates imposed on the domestic economy by foreign financial conditions reduced domestic money demand, which would normally be accommodated by central bank sales of foreign exchange, with the effect of retiring high powered money, and, via the money multiplier, reducing the money supply. Under fixed exchange rates, the full government spending multiplier applies, since interest rates do not rise. GDP rises by 2500, from 13000 to 15500. Fiscal policy is potent under fixed exchange rates. The interest rate remains at 10, so the demand for money rises by (0.5) ×2500=1250, and supply is accommodated in the process of central bank interventions to prevent an appreciation. When E = 0.5 we know from the other exercises 8 that Y = 7250. When the interest rate i* increases, output in the economy will drop, because the IS curve and the financial integration line determine equilibrium. The LM curve moves endogenously. The interest rate increases to i = 15% and output decreases to Y = 5250.

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When the exchange rate is allowed to float, the money supply a policy instrument, and LM curve and the financial integration determine output. An increase in i* then increases output, because it induces a depreciation and a rightward shift in the IS-curve. 9. (a) The increase in public spending shifts the IS curve rightwards. All previous points along the old IS curve now correspond to excess demand for goods, so the new curve lies above and to the right of the old one. The economy moves from point A to point B in Figure S11.9 below (see also Figure 11.14 in the textbook). (b) However, at the time Germany participated in the European Monetary System, a fixed exchange rate regime, so monetary authorities were expected to accommodate the increase in money demand through a higher money supply. The economy should move further to point C. If the Bundesbank resists the increase in liquidity in the banking system by sterilizing the inflows, interest rates remain above European levels, and capital inflows continue. The decision not to allow an increase in the money supply is consistent with fixed exchange rates only to the extent that the Bundesbank can continue to sterilize its foreign exchange purchases with other sales on the open market. In other European countries, the upward shift of the financial integration line induced by German unification forces monetary authorities to contract the money supply. The relevant figure in the textbook is Fig. 11.16 on p. 265 . Interest rate i LM B i* A C

IS' IS Output Y

Figure S11.9

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Chapter 12 1. Denote byU the true equilibrium rate of unemployment. Starting fromU,π=π0, the government incorrectly estimates U0 <U and tries to expand demand, using conventional means, to reduce unemployment to U0. Initially the economy moves along the short run Phillips curve. To reduce unemployment to U0 the government must accept an inflation rate π1 above the core inflation rate π0, as it moves the economy from point A to point B in Figure S12.1. But as soon as agents recognize this, core inflation is revised upwards (the backward-looking component of core inflation catches up) and the short-run Phillips curve is shifted upwards. The government can still keep the unemployment rate at U0, however, at the cost of a still higher inflation rate π2 (point C). Thus, inflation must keep increasing forever, which is evidently not sustainable. Eventually, the unemployment rate must go back to its equilibrium level, which is independent of monetary forces. The long-run outcome of an attempt to lower unemployment below equilibrium is a high inflation rate without any impact on the labour market. How in fact the government executes these policies is the subject of the next chapter. Inflation π π2 π1 π0 U0 U Unemployment rate U Figure S12.1 3. (a) The Phillips curve is described by a negatively sloped function:

π -π = - 10 (U -U) + s

It is assumed here that there are no supply shocks, that is, s=0. The following values can be calculated: ⇒ π = 14% when U = 6% ⇒ π =π = 4% U = U = 7%. ⇒ π = 2% U = 7.2% When core inflation increases the curve shifts up, so that it goes through the points:

C

B

A PC

22


⇒ π = 16% when U = 6% ⇒ π =π = 6% U = U = 7%. ⇒ π = 4% U = 7.2% 5. A depreciation raises the price of imported goods, especially raw materials and energy, which are used as inputs in the production process. This increases non-labour costs. For net oil importer countries, depreciation vis-a-vis the dollar (oil contracts are denominated in dollars) raises significantly non-labour costs and, ultimately, inflation. This explains why popular wisdom asserts that the best way to fight inflation is a strong currency. In an economy with flexible exchange rates, expansionary fiscal policy induces an appreciation of the currency, which reduce the cost of imported goods and acts as a good supply shock (s<0). 7. As implied by standard theory, deviations of unemployment from the equilibrium rate are related to deviations of actual inflation from core inflation, but under rational expectations, core inflation reflects all available information. Thus, deviations of actual from core inflation are related to new information which was not available when expectations were formulated. This sharp conclusion may be modified if labour contracts are concluded over several periods, or originate in several periods and are overlapping; under these circumstances the backward looking element of core inflation is still rational, but from the perspective of previous periods only, since meanwhile new and potentially useful information has arrived. Over time, the core rate will reflect this information also. As agents learn that their regime is characterized by higher and more variable inflation, they will shorten the contract period, making core inflation more forward than backward-looking. 9. Credibility shields the core inflation rate from temporary one-off shocks to the price level. For example, a shock to commodity prices pushes the Phillips curve upwards. To reduce the inflationary impact, the central bank may be tempted to tighten monetary policy to put downward pressure on labour costs. They may allow the domestic currency to appreciate, which further helps reduce the price of commodities imported. If people know that the inflation rate will not be allowed to increase, they do not revise their expectations of future inflation. Therefore, the short-run Phillips curve reverts quickly to its original position once the commodity price hike has passed. If instead the central bank is known to be little concerned by inflation, expectations that inflation will rise push up the core inflation rate and the Phillips curve shifts for two reasons: the increase in commodity prices and higher core inflation.

23


Chapter 13 1. The effectiveness of monetary and fiscal policy in an open economy with highly mobile capital is crucially dependent on the exchange rate regime. Thus, the parameter γ attached to monetary growth will be equal to 0 if there is a fixed exchange rate regime, and positive in a flexible rate regime. Similarly, φ will be positive in a regime of fixed exchange rates, but zero in a regime of floating rates. The parameter β will have two different interpretations (or meanings) in the two cases. In the fixed rate case, it stands for the effect that inflation has on international competitiveness and the effect that competitiveness has on aggregate demand by shifting the IS curve. In the floating rate case, it reflects the effect of inflation on the real money supply, and money market equilibrium, and influences aggregate demand via the interest rate channel (moving along the IS curve). 3. (i) A one-off increase in government spending (without any change in monetary policy). Under flexible exchange rates an increase in government spending will have no effect, since the appreciation in the real exchange rate will crowd out net exports (the PCA will decline) until aggregate demand has recovered its original position. In the more interesting fixed rate case, we can look at Figure S13.3(a) for the outcome. The AD curve shifts rightward as only fiscal policy matters: the economy reaches point B where inflation and output rise, but returns to its initial position, because world inflation is unchanged and because the fiscal policy move is only temporary. As core inflation - tracking actual inflation - rises, the AS curve shifts upwards and the transition path goes through point C where inflation is above the rate abroad, and output below trend, leading back to equilibrium in A. Inflation π AS´ AS C B π* A PPP AD´ AD

0 Output gap Y - Y Figure S13.3 (a) (ii) A permanent increase in money growth. An increase in µ will have no effect under fixed exchange rates, since it will be offset by central bank interventions to reverse its effect on local liquidity and interest rate conditions. A complete discussion of this is given in Section 13.2.4. (Of course, if continued unabated, such a policy is likely to threaten the existence of the fixed exchange rate regime, but this is a different question!). Under flexible exchange rates such a policy will shift the AD curve as in Figure S13.3(b), since its position in the AD-AS diagram is determined exclusively by the growth rate of money supply. If the

24


monetary expansion is permanent, the growth rate of money supply is permanently increased and the AD curve stays at AD´. The economy will converge to point C through successive shifts of the short-run AS curve. Inflation π C AS B A AD´ AD

0 Output gap Y -Y Figure S13.3 (b) 5. This question is reminiscent of Exercise 1 in Chapter 12. Under flexible exchange rates, the position of the AD curve is determined by the growth rate of money supply. Increasing this growth rate shifts the AD curve rightwards in Figure S13.5. In the short run, inflation and output rise (point B) As core inflation moves towards actual inflation, the AS curve shifts upward. The output gap is reduced and inflation increases (point C). The only way for the government to keep stimulating the economy is to raise again the rate of money growth (point D), and so on. Prices and money must grow increasingly faster: inflation increases. Such a policy is doomed to failure. As agents recognize more rapidly that the government is continuously shifting the AD curve, core inflation catches up faster with actual inflation. Such policies, if not terminated, can end in hyperinflation. Inflation π D AS´ C AS B A AD´´ AD´ AD

0 Output gap Y -Y Figure S13.5 7. A currency board is one of the most credible form of fixed exchange rate regimes, since it removes discretion and “cheating”, and subordinates monetary policy to the administration of

25


the fixed parity, at least in principle. Monetary policy is completely passive; in many instances, there is no central bank at all. This means that over the long haul, the inflation rate at home will equal that of the currency to which the currency board is linked. Consider a stabilization episode depicted in Figure S13.7. The economy is at point A, with a correctly anticipated high inflation rate π. Announcing and executing a policy of sharply reduced monetary growth in a flexible exchange rate regime with a weakly credible central bank would drive the economy into a deep recession, to point B. This is because agents are justifiably sceptical about the long-term viability of such a policy, and core inflation remains at its previous high level. Pegging the exchange rate credibly to a low inflation currency (the DM, Euro, or US dollar) signals a new regime. If the new regime is believed, inflation expectations will be lower and the AS curve will reflect this in the sense that core inflationπ is lower (in the figure, equal to π1. Because a currency board removes central bank discretion and presumably its ability to react to political pressure, expected and actual inflation should be lower than under a simple fixed exchange rate regime. In many cases, this approach has proved successful; Estonia is a widely cited case. On the other hand, the case of Argentina proves that the introduction of a currency board is useful only as a flanking manoeuvre; in the end, the stabilizing country must undertake credible actions that signal that reform has taken place that will prevent future inflation. In the case of Argentina, the government failed to exploit the initial success in fighting inflation to open up the economy to foreign trade and to cut government spending. It is evident that continued expansionary fiscal policy – ostensibly with the resources of international lenders – was responsible for a further deterioration of Argentina’s competitiveness (domestic inflation continued to run ahead of US dollar inflation). The private sector eventually lost faith that the currency board could be maintained, since the fiscal restraint required in times of crisis commanded little political support. A currency board is therefore only as good as the trust it generates, and only as long as it is expected to be maintained. As soon as the credibility of the currency board evaporates, the economy is back to square one (point A). Inflation π AS π0 A AS´ B AD π1 C AD´

0 Output gap Y -Y Figure S13.7

26


9. (a) Suppose the increase is temporary. In Figure S13.9 below, this corresponds to a shift of the PPP line consistent with the higher inflation rate π*´ and a rightward shift in the AD curve to AD´. As a result, Dutch inflation increases from π* to π´ and there is an increase in output (B). This is precisely what happened immediately following German reunification in the period 1990-2. Inflation π AS´ C AS π*´ PPP´ B π* A PPP AD´ AD

0 Output gap Y -Y Figure S13.9 The Netherlands can fight inflation and curtail the boom in the short run by revaluing against the Deutschmark, effectively offsetting the rightward shift of the AD curve by increasing the real exchange rate. Since this is a one-off move, it would only be appropriate to fight a one-off increase in German inflation. The result, in principle, could keep the Dutch economy at point A. Since the increase was temporary, the PPP curve does not shift permanently so inflation will return to its original value anyway, but restrictive demand policy could fight inflation even in the short run. (b) In the case of a permanent increase in German inflation, the AD curve and the PPP curve shift permanently upward to the position showed in the figure. The long run corresponds to point C in Figure S13.9 where Dutch inflation is permanently higher and output is on its trend growth path. In the short run, higher inflation in Germany leads to a real exchange rate depreciation for the Netherlands. This gain in competitiveness vis-a-vis a key trading partner has the effect of shifting the AD curve to the right: at point B output and inflation have risen. The Netherlands may try to prevent the inflation rate from rising by revaluing their currency against the Deutschmark. However, in the long run, PPP requires that inflation rates will be equal, unless these revaluations occur regularly, or if the fixed rate regime is abandoned.

27


Chapter 14 1. A permanent decline in the foreign rate of inflation implies that, ceteris paribus, home products become less competitive over time (or equivalently that foreign goods become more competitive). As long as the exchange rate does not change, expenditures are shifted towards foreign products. The AD curve shifts to the left and actual inflation falls. Gradually core inflation decreases as well, resulting in a movement of the AS schedule to the right. Output increases again and inflation at home slows down also in relation to the foreign economies. In the end both economies will ultimately return to their original level of output yet at a lower rate of inflation.

3. One observes a shift of the LAS and the AS curves to the right (given the fiscal and monetary policies), output rises. Since the new technology allows the production of more output with the same amount of inputs, wealth rises. It is likely that investment will increase as well, since the productivity of capital has risen. These effects imply a shift of the AD curve to the right. If the shock is permanent, the economy stays at this higher equilibrium output level. However, if technology improves temporarily, the whole process moves into the opposite direction again. Furthermore, the stance of monetary policy will affect the propagation of the shock.

In the real business cycle paradigm, the transmission mechanisms are somewhat different, and some implications are counterfactual. Real wages and interest rates rise upon impact of the technology shock, leading to some intertemporal substitution of labour for leisure in the period surrounding the shock. However, a wealth effect resulting from the shock will work to reduce labour supply, as households demand more leisure (this may be weakened by additional assumptions concerning utility). In addition, the effect on output and employment of the shock is independent of monetary policy, since the monetary sector does not influence the real sector in this model.

5. (i).In all simulation in exercises (i)-(iii), the same shock sequence was used. The following output for time periods 1 to 50 is generated for the stochastic difference equation:

x(t)=1.3x(t-1)-0.5x(t-2)+ε(t)

-3-2-1012345

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

time

x

28


Here, roughly four full cycles are observed (naturally, this answer will differ across coin-toss sequences but on average should hold!) The roots of the difference equation are given by λ1,2

=0.65 ±0.28i with |λi| =0.70 for i=1,2.

5(ii) In the second example, the frequency of the cycles rises. One can observe roughly six cycles over the same period. The roots of the difference equation are given by λ1,2 =0.65 ±0.69i with |λi| =0.95 for i=1,2. Intuitively, shocks in case (ii) seems to work themselves out more quickly, giving less chance for shocks to cumulate into longer, persistent cycles.

x(t)=1.3x(t-1)-0.9x(t-2)+ε(t)

-6

-4

-2

0

2

4

6

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

time

x

5(iii) In this case the stationary cyclical pattern is less easy to detect. The variable seems to wander without a tendency to return to its origin (the value 0). In fact, such variables are said to be nonstationary.

x(t)=1.3x(t-1)-0.3x(t-2)+ε(t)

-2

0

2

4

6

8

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

time

x

The roots of the difference equation are given by λ1,=0.30 and λ2 =1.00. Since one root is no longer inside the unit circle, the difference equation becomes unstable. Intuitively, the pattern of coefficients does not "force" the economy to return to its starting point after being temporarily shocked.

7. In the Burns-Mitchell diagram in Figure 14.4(a), total consumption exhibits only a slight cyclical pattern. If only nondurables (i.e. food) were considered instead, the cycle would be

29


even less visible. However, durables are generally not bought every period (unlike food, drink and services). Consider the purchase of a new TV set or car, which can be readily postponed over time. If the economy falls into a recession, households often put off purchases of these goods. This is the origin of the cyclical behaviour of durables. One would thus expect a much more pronounced peak such as that found in Figure 14.4(b). This is exactly what Burns and Mitchell found in their work.

9. The wealth effect reduces (home) consumption, the IS curve shifts to the left. With fixed exchange rates, the new situation will be exacerbated. As the central bank fights pressure to depreciate by tightening monetary policy and shifting the LM curve to the left, it depresses output even further. If Sweden would have been operating under a floating exchange rate regime, the initial shift of the IS-curve would have led to a depreciation. This would have increased exports, cut imports and shifted the IS-curve towards its original position. Output would have fluctuated less in a flexible exchange rate regime.

30


Chapter 15 1. Progressive taxation allows governments to redistribute wealth and income among economic agents and thereby reduce inequality. There are many philosophical issues involved, including the notion of the philosopher John Rawls that under a "veil of ignorance" concerning future income and wealth, individuals would prefer a form of insurance against very low earnings. It also corresponds vaguely to notions that "ability to pay" should be a primary consideration in assessing individuals' tax liabilities. Another feature of progressive income taxes is their function as automatic stabilizers. Cyclical fluctuations affect the income tax directly. Consider the effect of a recession. We may think that the whole range of incomes is shifted downwards (in other words, everyone earns less). In this case aggregate taxes are a convex function (with increasing slope) of aggregate income. Therefore, when output falls, taxes fall more than proportionally. This need not be the case: suppose that during a recession, the poor become poorer and rich become richer in such a way that when aggregate income falls, tax revenues may actually increase! Normally one rules this out by hypothesizing that the economy moves homothetically. 3. The national debt is frequently an emotional issue. This can be seen in the 1992 US presidential election, the debate over the financing of German unification, and most recently in the fiscal requirements of the Maastricht Treaty and later the Stability and Growth Pact. The statement that the debt will never be repaid is an excellent example of the fallacy of composition: what is true for the sum of individuals need not be true for each individual. For the great majority of countries and historical episodes, each individual creditor has been repaid the nominal amount which he or she lent the government plus interest. The representative individual is content to lend to the government and expects to be repaid over his lifetime. The debt serves as a means by which the public can save, either for retirement, for a rainy day, or against future tax liabilities. In the extreme case of Ricardian equivalence we know that the national debt does not represent wealth at all, which implies that it is not a net liability either. In this view the public has fully anticipated and discounted its future tax liabilities against the government debt it owns. Of course, someone must deliver the principal and interest when government borrowing comes due: this resources are obtained via higher taxes, economic growth (with a larger tax base), borrowing from other individuals, or monetisation. The central feature one needs to follow is the sustainability of the debt, and for this reason the debt/GDP ratio is widely followed. The national debt is not a scam as long as each individual's debt contract is honoured and the government meets its aggregate intertemporal budget constraint. For some countries, however, this is already a serious challenge. 5. The monetary aggregate (M1 or M2) is central bank money (M0) multiplied by the money multiplier. Under the condition that the public holds no currency the money multiplier is simply (recall Chapter 9):

M1/M0 = 1/rr

31


Velocity is defined as V = PY/M. If velocity increases while holding prices (P) and GDP (Y) constant, the monetary aggregate has to fall. Hence, the demand for central bank money will also fall, reducing the tax base for seigniorage. Velocity is generally a positive function of the nominal interest rate, which in turn is a positive function of the expected rate of inflation. It is for this reason that in hyperinflations velocity tends to rise so high that the tax base goes to zero. 7. No, strictly speaking, banknotes are liabilities of the central bank. See Chapters 8 and 9 for more details. It is possible to consolidate the central bank with the government if the latter indeed owns the former (in the case of the ECB this is obviously not entirely true!) If one did consolidate the central bank with the central government, it follows that their collective obligations vis-à-vis the private household, corporate and banking sectors could be considered as debt, with the difference being that currency normally bears no interest.

9. Using the fact that Hdt

dH 1== µπ and )exp(/ αµ−= APH

)/()/

, long run seigniorage can be

rewritten as ( )exp()exp()(/)(/ )/(()/1 αµµαπµµ −=−=== dtdHP AAHdtdH PHPH . Thus, seigniorage is a function of central bank money growth (µ) for two reasons. Given the money holdings of the private sector, an increase in monetary growth increases seigniorage, since this money is used to purchase real resources for the state. At the same time, higher central bank money growth will increase inflation, so people will tend to hold fewer real balances, reducing the tax base on which seigniorage is set. In this particular case, we can use calculus to help understand this dependence. The first derivative of )exp( αµµ −A with respect to µ is )exp()exp( αµαµαµ −−− AA ; the first part corresponds to the increase in revenues due to an increase in the tax rate while the second reflects the shrinking tax base. Set this expression to zero to obtain an optimum and simplify to obtain

1−= αµ or that the seigniorage-maximizing inflation and monetary growth rate is the inverse of the elasticity of the demand for money. (Check that the second derivative of seigniorage is negative, so we indeed have a maximum). In Chapter 17 we will recognize this as an application of the Ramsey Principle of public finance: tax those items most heavily for which the demand is most inelastic.

32


Chapter 16 1. In principle, the real interest rate reflects the probability that a borrower will not meet its obligations: a premium compensates the lender for this risk compared with low-risk loans. What matters for public debt, therefore, is whether the government is violating its intertemporal budget constraint. The debt stock itself is insufficient evidence to pass judgment on this issue. In principle, a government can stabilize any debt (that is, the stock) by running an appropriate primary budget surplus (that is, the flow), as long as the tax base is available. The deficit is a crucial indicator of sustainability because 1) it indicates whether the debt is currently growing without bounds; 2) it shows whether or not the existing debt is close to being stabilized. Yet it is not sufficient, since a sufficiently large primary surplus is the condition for stabilization; information on debt service (interest payments) are crucial. 3. If seigniorage is ruled out, rapidly rising debt could signal that a country is violating its intertemporal budget constraint. This violation could lead to the expectation that the country is indeed likely to resort to seigniorage, which means that inflation rates would likely rise in the future. If this expected future rise in the price level is large, agents may start to raise prices now in expectation of a hyperinflation later. 5. Monetary policy is endogenous with fixed exchange rates, because the central bank has to intervene in the foreign exchange markets to keep the exchange rate constant. As soon as the exchange rate starts to deviate from the fixed parity the central bank buys or sells own currency in exchange for foreign currencies. This influences directly money supply and thus interest rates without major lags. Without knowing more about firms’ expectations about future demand conditions and the current economic situation no further statements about the working through of these interest rate changes to the labour and goods markets can be made. It may take some time until investment and consumption react to lower interest rates. With flexible exchange rates, money supply is exogenous and the central bank's policies are not bound by exchange rate interventions. The effectiveness of expansionary or restrictive policies depend rather on the monetary instrument used. Those instruments that directly influence money supply, like open market interventions or monetisation of the public debt, should have the same direct effects on the interest rate as purchasing or selling foreign exchange. Measures that only influence the possibility of commercial banks to obtain credit from the central bank, like changing the discount rate, are likely to take longer to work via the interest rate. Commercial banks have to change the interest they charge on credit and the amount of credit granted has to be changed before the money supply increases. 7. Both policies are faced with the problem that the need for policy intervention has first to be discovered (recognition lag). However, the decision, implementation and effectiveness lags are very likely to differ. (a) Fiscal policy: Governments need time to form decisions, pass and implement new legislation. This can take up a considerable amount of time. However, once government expenditure or taxation are changed, they have usually a direct effect on aggregate demand, output and unemployment. There are exceptions to this, when for example increases in government expenditure lead to increases in savings (Ricardian equivalence theorem) offsetting real effect of the policy change.

33


(b) Monetary policy: The decision and implementation lags for central bank policy are very short. Central banks may very frequently change the discount rate, buy or sell bonds in the open market or intervene in foreign exchange markets. The effectiveness of these policies on the real sector of the economy depends on how strongly investment and consumption react to changing conditions in money markets and may take longer to change output and employment than direct government expenditures. 9. This is the reliquification phenomenon which was explained in Chapter 8, Box 8.5. When inflation rises, nominal interest rates rise, and real money demand falls. As soon as hyperinflation disappears, interest rates fall, and the real money demand rises, as people regain trust in the national money. Additional evidence is provided by the exchange rate: if the exchange rate keeps depreciating, the hyperinflation episode may not be over. This was not the case in Bolivia.

34


Chapter 17 1. As always, it is crucial to distinguish between the two exchange rate regimes. It is important to note that in the following figures the horizontal axis represents absolute output levels, not the output gaps. Fixed exchange rate case: In Figure S17.1 (a) the long-run aggregate supply curve shifts to the left from LAS* to LAS** corresponding to the old and new trend output Y* and Y**, respectively. The new long-run equilibrium can be fully characterized using the foreign inflation rate π* (point C). The short run is described by the AS curve associated with LAS** and by the AD curve. The latter may be slower to adjust if agents take time to recognize that their wealth level has been reduced and that they have to permanently reduce spending. The economy moves to point B, where inflation is above its long-run level and where output falls because the real exchange rate appreciates and the economy's competitiveness declines. After the transition the economy has to end up in C. The dynamic path to point C may become somewhat complex, as the AS curve shifts leftward (core inflation catches up with actual inflation), and the AD curve may also shift. If the AD curve adjusts immediately to its new equilibrium value, there are no dynamics: the economy jumps from point A to point C. Flexible exchange rate case: As in the fixed rate case, the long-run supply curve shifts to the left from LAS* to LAS** (Figure S17.1(a)). Long-run inflation is now determined by the domestically determined rate of money growth (µ* in the diagram). As long as the long-run rate of growth and the money growth rate are unchanged, the long-run inflation rate does not change. In the long run, the AD will shift to the left, so that money growth and inflation are consistent and correctly anticipated. Under these assumptions the short and long run effects are the same as under fixed exchange rates. The dynamics will also be similar but the mechanism is different. Now inflation leads to nominal depreciation and to a reduction in the real money supply. High nominal and real interest rates depress demand and the AD curve gradually moves to the left until it stabilizes at point C in Figure S17.1 (b). Inflation LAS** LAS* AS** AS* B π* C A AD Y** Y* Output Y In the flexible exchange rate case, a permanent increase in the rate of inflation could occur if the government misunderstood the decrease in equilibrium output and tried to stop the decline

35


in output with a permanently expansionary monetary policy. In a fixed rate regime, the money supply is endogenous and such a situation cannot arise. Inflation π LAS** LAS* AS** AS* µ* C A

AD* Y** Y* Output Y Figure S17.1 (a) and (b) 3. The effect of shifting out the collective labour supply curve is illustrated by the shift from LS,COL to LS,COL´ in Figure S17.3 on the next page. The critical effect is to increase aggregate employment, lower real wages (per person employed), and raise output consistent with general equilibrium in all markets. With otherwise flexible prices, this increase in output will be demanded by households, but only after the price level has declined enough to increase real balances, given nominal money supply. In this example, we assumed that the real interest rate remains unchanged across the two equilibria, but you may consider as an exercise the consequences of an increase in equilibrium interest rates accompanying the shift (meaning IS and LM intersect at a different point than before). Note that as a consequence of wage moderation, unemployment (given by the bold arrows in the first panel) unambiguously declines. 5. Gasoline demand and labour supply are more inelastic than jewelry demand and capital services, respectively. According to the Ramsey principle, the former should thus be taxed more heavily than the latter. Note that the Ramsey principle can lead to politically difficult situations: necessities such as food, fuel and housing are all characterized by low price elasticities of demand. Taxing these necessities heavily leads to severe inequality across individuals in society, and this may be unacceptable to a majority of voters. 7. For background, please read Section 7.4.3. By subsidizing manufacturing industry, Norway was able to prevent the exchange rate appreciation which characterizes the Dutch disease and hurts domestic competitiveness. (For details on the Dutch disease, see Webbox 7.2.) This loss of competitiveness will reduce the importance of the traded goods sector for a long time. Especially if the Dutch disease is perceived as being temporary (as in the case of Holland) and if large costs of adjustment are associated with shrinking the traded goods sector, such a

36


policy may be good supply side policy as well. One should not forget the fact that it is always difficult to dismantle subsidies after they are put into place, however. 9. This is a tricky question: If workers in trade unions hold higher paying jobs by merit of the monopolistic supply of labour to the market, then dismantling those unions or reforming labour markets in general will lead to losses for them and is likely to be resisted fiercely. If their underlying productivity in their job and especially in alternative jobs is the reason for their higher pay, then this argument does not hold. It is a matter for the data to decide. Real Wage LS,Coll LS,Coll´

LS,Households w w´ i LD

L L´ Employment Output Output Output (b) F 45° L L´ Employment Output

Y*

Y’

Y Y´

Interest rate

R M/P (M/P)´ eal balances

Prices

P

Interest rate

M

M

R M/P (M/P)´ eal balances

S S´

IS IS´ LM LM´

P´

L(Y,i,c) L(Y´,i,c)

Y Y´

Y’

Figure S17.3

37


Chapter 18 1. Re-read the chapter! 3. This is not a question about the Phillips curve! Inflation acts as a tax. Furthermore, the higher inflation is, the more uncertain it becomes, clouding long-run planning by firms and households, an effect akin to a reduction in property rights. Thus we expect inflation to harm growth. 5. Nobody wants to grant permanent monopoly, that would stifle competition. And anyway, most innovations eventually become old hat.


Chapter 19 1.a) Curiously, insider trading can represent an important mechanism for conveying new information which is otherwise unavailable to the market. With insider trading, prices will more rapidly reflect new information which is unavailable to the public. This increases market efficiency. At the same time, insiders generally earn abnormal profits (they 'beat' the market), which means that non-informed traders will lose on average. The information asymmetry systematically put outsiders at a disadvantage. The increased perceived overall riskiness is likely to lead to higher bid-ask spreads, reduce liquidity and increase transaction costs. It can be thought of as a "tax" on trading. Finally, there is a potential conflict of interest for firm managers, who have a fiduciary responsibility to shareholders. If they were allowed to trade in an unrestricted way, they could easily earn large fortunes by manipulating the timing of announcements and other events and trading on this basis. (b) Participants in a foreign exchange market are physically unidentifiable, since there is no physical presence and transactions may occur all over the world. Moreover, the daily turnover on exchange markets is extremely high. Tracing insider trading would be very difficult if not impossible. Finally, in foreign exchange markets, government institutions, such as central banks, often intervene (using insider knowledge) to achieve policy objectives. 3. a) Starting with €1m (one million), consider buying $1m, then using these dollars to purchase yen to yield ¥115 m. Yen purchased this way are more expensive than using €1 m to buy yen directly, which would yield ¥120 m. A profitable arbitrage opportunity arises: purchase yen with euros directly, convert these yen into dollars, and then convert these dollars back into euros. The profit is easy to calculate; for each euro invested the return is (¥120/€)/(¥115/$)=1.04348$/€, or about 4.35%. The market is likely to sell Euros into yen directly, appreciating the ¥ vis-à-vis the €, and buy $ with ¥, appreciating the former with respect to the latter. Or the € might appreciate with respect to the dollar. An number of combinations of these can lead to the elimination of triangular arbitrage opportunities. b) With a bid-ask spread, the situation changes. It now matters whether purchases or sales are being made; that is, the direction of trading will matter. The strategy discussed in a) will now yield (¥118/€)/(¥117/$)/($1.01/€) = 0.99856 for every euro invested, which is obviously not profitable. Just to be sure, one should check whether the other option is profitable: could we use euros to buy dollars, then use the dollars to buy into yen, which are then used to buy euros again? This strategy yields for each euro (0.99$/€)(¥113/$)/(¥122/€)=0.9170, which is not profitable either. 5. To keep things simple, consider the version of the theory without explicit uncertainty, so that the uncovered interest parity condition allowing for a risk premium can be


expressed in non-approximated form as (1+i*) = t

t

SS 1+ (1+i)(1+ ψt), where ψ represents

the premium required on investing in the foreign asset (relative to the home yield i). Note that the risk premium may indeed vary over time. Now rearrange to obtain

( )( )

( ) 1*111

++++

=S tt

ttt S

ii ψ

,

or, substituting recursively, n times:

( )( )( )

( )( )( )

( )( )( )

( )( )( ) 1**

2

22*

1

11* 1

11....

111

111

111

+++

++

+

++

+

++

+++

+++

+++

+++

= ntnt

ntnt

t

tt

t

tt

t

ttt S

ii

ii

ii

ii

Sψψψψ

.

The formula shows that for a given expectation of the terminal or long run exchange rate, an increase in the risk premium on foreign comparable assets leads to an appreciation (rise in S) of the domestic currency. 7. As evident from Figure 19.9, the internet boom took place over a relatively brief period (1998-2000) just as did the Tulipmania described by MacKay in Box 19.5. A signature of this episode is the apparent disavowal by market participants of all rules of the game in favour of the view of the “new economy” – despite the fact that most shares never paid a dividend nor even showed sustainable earnings. (Incidentally there are wonderful quotations of Irving Fisher in 1928-1929 maintaining the same thing about the US economy at the time, just before the crash of October 1929 ruined him!) Such behaviour can only be explained by widespread beliefs that the boom will persist and that traders could liquidate their positions in time to make a profit. From the point of view of an individual trader, if the expected yield, as well as the perceived probability of successful and timely unwinding of long positions is high enough, it is rational to continue to invest even if it is clear that the game of hot-potato must have some end. The potential for collateral damage from the collapse of a bubble is evident: the balance sheets of financial institutions which helped fund these investments will be hurt. This will have negative implications for the liquidity and even solvency of the banking sector. It is for this reason that central banks monitor such bubbles carefully and make contingency plans to fight crises in their aftermath (recall US Federal Reserve Chairman Greenspan’s criticism of “speculative exuberance” in the late 1990s). To the extent that households perceive higher valuations of shares as increases in wealth on the upswing, a stock market collapse in internet stocks will have negative ramifications for consumption spending, and the collapse of the market for new stock issues may make external equity financing of investment projects more difficult. 9.(a) We obtain the MM curve by rearranging the equation for money market equilibrium

40


++= + )/30000Y0.5 -/( *1

11

ttttt PMi

SS

and for St+1=1, Y = 8000 and i* = 0.04:

( ) Y0.5 -/*13000030000

ttt PMi

S++

=

( ) 0004 -/1.043000030000

ttt PM

S+

=

In Figure 19.9(a) below this upward-sloping MM schedule is plotted for M=2000 and M=3000. When the money supply increases from 2000 to 3000, the MM schedule shifts downwards, reflecting the necessity of either a depreciated exchange rate or increased price level or both, to clear the money market, given the static expectation of the exchange rate in the subsequent period.

0

0.5

1

1.5

2

2.5

3

P 0.4 0.65 0.9 1.1

5 1.4 1.65 1.9

Price Level (P)

Nom

inal

Exc

hang

e R

ate

(S)

MM(2000)

MM(3000)

GG

A

Figure 19.9 (a) (b) Recall the definition of the real exchange rate σ=SP/P*. For given values of P* and σ, the GG schedule is described by the hyperbola 0.5= StPt as shown in figure. The long-run equilibrium for M=2000 is given by point A.

(c) There are in fact two ways to answer this question. The first, corresponding to static, myopic expectations, assumes that St+1 is equal to 1 throughout, for both values of the money supply. This, however is inconsistent with rational expectations, since in a scenario with higher money supply, the long-run nominal exchange rate must be lower and the

(d) price level must be higher (monetary neutrality!). A more appropriate alternative, which we adopt, is that agents in the economy have rational expectations, meaning in this case that their long-run anticipation of the price

41

Answers to Odd-Numbered Exercises Burda/Wyplosz Macroeconomics: A European Text Chapter 19 level is correct. To do this, we need to work backwards: In the long run (or the second period), S is constant, so (St+1 − St)/St=0. This means that the long-run price level must be uniquely pinned down by the money supply from the money market equilibrium condition:

[ ] 75

0.04)(30000)(40002000

*30000Y0.5=

−=

−=

iMP

From the GG condition this means that the long-run nominal exchange rate must be given by 0.5= SP and thus equals 7/10 (because 0.5/(5/7)=7/10). This condition pins down the long-run exchange rate consistent with the uncovered interest rate parity. Using St+1 =0.7 we can proceed and plot the MM condition. For a higher money supply M=3000 the price level will then be given as above by 15/14 and the exchange rate by 0.5/(15/14)=7/15. (this can be verified by the fact that the new exchange rate is 50% lower than the initial value, corresponding to an increase of money and prices by 50%). Thus the MM schedules corresponding to M=2000 and M=3000 must pass through the GG schedule at nominal exchange rates 7/10 and 7/15, their respective values for St+1. These points A and C are drawn with the GG curves in the figure below.

0

0.5

1

1.5

2

2.5

3

0.2 0.45 0.7 0.9

5 1.2 1.45 1.7 1.9

5

Price Level (P)

Nom

inal

Exc

hang

e R

ate

(S)

MM(2000)

MM(3000)

GG

A

C B

Figure 19.9(b) (d) With prices rigid in the short run, a one-off increase in money supply moves the economy instantaneously from A to B in Figure S19.9(b). The exchange rate depreciates immediately below its long-run equilibrium value, so that the ensuing expected appreciation (S rising) sufficiently offsets the lower domestic interest rate and restores money market equilibrium. This is the famous “overshooting” result first described by Rudiger Dornbusch (R. Dornbusch “Expectations and Exchange Rate Dynamics” JPE (1976). As prices increase gradually (excess demand of domestic goods), real money balances are reduced. To maintain money market equilibrium, the interest rate increases, requiring an exchange rate appreciation from B to its long-run equilibrium level C. Since money market equilibrium is holding continuously over this time, the economy moves along the new MM curve corresponding to the money supply M=3000. Note that the model solved under static expectations (holding St+1=1 throughout) may result in overshooting, but will not be consistent with monetary neutrality in the long run.

42


Chapter 20 1. The SDR is used alongside other currencies, chiefly the US dollar. It is not managed by a world central bank so increases in its supply are only allowed episodically. The bancor would have removed the monetary domination of one country, the US. 3. Beggar-thy-neighbour policies are exchange rate devaluations designed to gain a competitive advantage. If all countries devalue vis-à-vis each other, no one actually succeeds, nothing is achieved. Tariff wars are similarly self-destructive (no gain in exports as protective tariffs go up everywhere) with a crucial difference: generalised high tariffs are effective at shutting down international trade. 5. Low growth: inflation has declined, but accumulated price increases since 1991 probably mean that the peso is now overvalued, hence low growth. Overvaluation means that somehow, either prices go down (and negative inflation is occurring) or a depreciation will have to be enacted. Given the costs of protracted deflation, the markets expect the latter, at some point. This means higher interest rates than in the US although, in principle, a currency board should deliver the same interest rate as in the anchor currency country. The problem is that a the 1:1 exchange rate cannot be changed without legislative approval. Such a debate would trigger massive speculation and is therefore discarded. Effectively Argentina is in a bind, hence the debate about an exit strategy. One strategy would be to dollarize, eliminating forever the threat of a devaluation, which would bring interest rates down. Argentina considered this possibility and asked the US for a fair share of seigniorage. As the US refused, the plan was dropped. There is still no clear exit strategy in view. [Authors’ note: This proposed solution was written some time ago. In the meantime, Argentina has gone off the deep edge, not only giving up the currency board, but also devaluing its currency and defaulting on its debt, plunging its economy into turmoil. As much as we regret the current situation in Argentina, we also feel vindicated in our assessment! ]

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