© 2009 Pearson Education Canada 3/1 Chapter 3 Demand Theory.

© 2009 Pearson Education Canada3/1

Chapter 3Chapter 3

Demand TheoryDemand Theory


The Budget ConstraintThe Budget Constraint

Attainable consumption bundlesAttainable consumption bundles are bundles that the consumer can are bundles that the consumer can afford to buy.afford to buy.

Attainable consumption bundles Attainable consumption bundles satisfy the following inequality known satisfy the following inequality known as the as the budget constraintbudget constraint..

pp11xx11 ++ pp22xx22 ≤ M ≤ M


Figure 3.1 Attainable consumption bundlesFigure 3.1 Attainable consumption bundles


Opportunity Cost, Real Income and Opportunity Cost, Real Income and Relative PricesRelative Prices

Rewriting the budget constraint by solving for XRewriting the budget constraint by solving for X2 2

gives:gives:x2 = M/p2 – (p1/p2)x1

Where:Where: M/pM/p2 2 is is real incomereal income

PP11/P/P22 is the is the relative pricerelative price

The The relative pricerelative price shows that the shows that the

opportunity costopportunity cost of good 1 is of good 1 is PP11/P/P22 units of units of

good 2. good 2. PP11/P/P22 is the absolute value of the slope of is the absolute value of the slope ofthe budget line.the budget line.


Endowments Rather Than MoneyEndowments Rather Than Money Sometimes an endowment of goods is Sometimes an endowment of goods is

assumed rather than cash.assumed rather than cash. Sally owns apples xSally owns apples x11

0 0 and eggs xand eggs x2200..

Her budget constraint is:Her budget constraint is:

pp11xx11 ++ pp22xx22 ≤ p ≤ p11xx110 + 0 + pp22xx22

00

Solving for Solving for xx2:2:

xx22 = (p = (p11xx110 + 0 + pp22xx22

0)0)/p/p2 2 – (p– (p11/p/p22)/x)/x11

As before, the budget constraint depends upon relative As before, the budget constraint depends upon relative

prices and real income (the endowment).prices and real income (the endowment).


Figure 3.2 The budget line with endowmentsFigure 3.2 The budget line with endowments


The Choice ProblemThe Choice Problem

The non-satiation assumption implies The non-satiation assumption implies that utility maximizing consumption lies that utility maximizing consumption lies on the budget line.on the budget line.

The consumer choice problem is:The consumer choice problem is:

maximize maximize U(xU(x11, x, x22)) by choice of by choice of xx1 1 & x& x22,,

subject to constraint subject to constraint pp11xx11 ++ pp22xx22 = M = M


The Choice ProblemThe Choice Problem

In principle we refer to the solutionIn principle we refer to the solution (x(x11**,,

xx22**)) as as endogenous variables, endogenous variables, as these as these

variables are determined within the variables are determined within the model.model.

The actual values of The actual values of XX11** and and XX22

** depend depend on the on the exogenous variables exogenous variables in the in the model, (model, (pp1, 1, pp22 and and MM) and on the specific ) and on the specific form of the utility function.form of the utility function.


Figure 3.3 Non-satiation and the utility-Figure 3.3 Non-satiation and the utility-maximizing consumption bundlemaximizing consumption bundle


Demand FunctionsDemand Functions

XX11* * = D= D11(p(p11, p, p22, M), M)

XX22* * = D= D22(p(p11, p, p22, M), M)

These These demand functiondemand function equations equations simply say that the choice of simply say that the choice of XX11

** and and XX22

** depend upon the prices of all depend upon the prices of all items in the consumption bundle and items in the consumption bundle and the budget devoted to that bundle.the budget devoted to that bundle.


Anna’s optimal choice when both Anna’s optimal choice when both goods are perfect substitutesgoods are perfect substitutes


Graphic Analysis of Utility MaximizationGraphic Analysis of Utility Maximization

Assume indifference curves are Assume indifference curves are smooth and strictly convex.smooth and strictly convex.

Interior solutionsInterior solutions are where are where quantities of both goods are positive.quantities of both goods are positive.

Corner solutionCorner solution is one where the is one where the quantity of one good is positive and quantity of one good is positive and the quantity of the other is zero.the quantity of the other is zero.


Interior SolutionInterior Solution

An An interior solutioninterior solution is described is described by:by:

1.1. PP11xx11** ++ PP22xx22

** ΞΞ M M, the optimal bundle , the optimal bundle lies on the budget line.lies on the budget line.

2.2. MRSMRS(X(X11**, X, X22

**) ) ΞΞ P P11/P/P22 , the slope of , the slope of the indifference curve equals the the indifference curve equals the slope of the budget line at the slope of the budget line at the optimal bundle.optimal bundle.


Figure 3.5 The utility-maximizing Figure 3.5 The utility-maximizing consumption bundleconsumption bundle


Figure 3.6 Essential goodsFigure 3.6 Essential goods


Corner SolutionsCorner Solutions

A A corner solutioncorner solution graphically lies not in graphically lies not in the interior between the two axis, but at a the interior between the two axis, but at a corner where the budget line intersects corner where the budget line intersects one of the two axes.one of the two axes.

For example, if at the point where the For example, if at the point where the budget line intersects the budget line intersects the XX22 axis, the axis, the budget line is steeper than the budget line is steeper than the indifference curve, only good 2 will be indifference curve, only good 2 will be purchased.purchased.


Figure 3.7 Inessential goodsFigure 3.7 Inessential goods


Excise Tax Versus Lump-Sum TaxExcise Tax Versus Lump-Sum Tax

Given a choice between a lump sum Given a choice between a lump sum tax and an excise tax that raises the tax and an excise tax that raises the same revenue, the consumer will same revenue, the consumer will choose the lump sum tax (see Figure choose the lump sum tax (see Figure 3.8).3.8).


Figure 3.8 Excise versus lump-sum taxesFigure 3.8 Excise versus lump-sum taxes


Figure 3.9 Cash transfer versus Figure 3.9 Cash transfer versus in-kind transfersin-kind transfers


Figure 3.10 Optimal Figure 3.10 Optimal consumption with endowmentsconsumption with endowments


Figure 3.11 Normal and inferior goodsFigure 3.11 Normal and inferior goods


Figure 3.12 Engel curvesFigure 3.12 Engel curves


Figure 3.13 The consumption response to a Figure 3.13 The consumption response to a

change in the price of another goodchange in the price of another good


Consumption Response to a Consumption Response to a Change in PriceChange in Price

The The price-consumptionprice-consumption path path connects the utility maximizing connects the utility maximizing bundles that arise from a change in bundles that arise from a change in the price of the price of pp1 1 or or pp22..

Note that when Note that when pp11 changes, changes, MM and and pp22

are assumed to be constant. Likewise are assumed to be constant. Likewise if if pp22 were to change, were to change, MM and and pp11 are are assumed to be constant.assumed to be constant.


Figure 3.14 The price-consumption Figure 3.14 The price-consumption path and the demand functionpath and the demand function


ElasticityElasticity

ElasticityElasticity is a measure of is a measure of responsiveness of the quantity responsiveness of the quantity demanded for one good to a change demanded for one good to a change in one of the exogenous variables: in one of the exogenous variables: price or income.price or income.


Figure 3.15 The need for a unit-free Figure 3.15 The need for a unit-free measure of responsivenessmeasure of responsiveness


Own-Price ElasticityOwn-Price Elasticity

Own-price elasticity (Own-price elasticity (EEllll)) relates to how relates to how much the one good changes when its own much the one good changes when its own price changes.price changes.

EEllll= % change in = % change in xx11 / / % change in % change in PP11

)/)(/( 111111 xppxE

)//()/( 1111 ppxxEll OR


ElasticityElasticity

If we allow changes in the exogenous If we allow changes in the exogenous variables to approach zero we obtain variables to approach zero we obtain marginalmarginal or or point elasticitypoint elasticity..


ElasticityElasticity Arc elasticityArc elasticity measures discrete changes measures discrete changes

in in xx11 when there is a discrete change in when there is a discrete change in pp11,p,p22 or or MM).).

By allowing changes in the exogenous By allowing changes in the exogenous variables to approach zero gives variables to approach zero gives marginalmarginal or or point elasticitypoint elasticity..

Price elasticity of demandPrice elasticity of demand for a good is for a good is the elasticity of quantity consumed per the elasticity of quantity consumed per capita with respect to the price of the capita with respect to the price of the good.good.


Income ElasticityIncome Elasticity

The The income elasticityincome elasticity of demand is of demand is the elasticity of quantity consumed the elasticity of quantity consumed per capita with respect to income per per capita with respect to income per capita.capita.


Income Elasticity FormulaIncome Elasticity Formula

)/)(/( 111 xMMxE m


Cross Price ElasticityCross Price Elasticity

The The cross price elasticity of cross price elasticity of demanddemand for good 1 with respect to for good 1 with respect to the price of good 2, is the elasticity the price of good 2, is the elasticity of per capita consumption of good 1 of per capita consumption of good 1 with respect to with respect to pp22. .


Cross Price Elasticity FormulaCross Price Elasticity Formula

)/)(/( 122112 xppxE

Date post:	26-Dec-2015
Category:	Documents
Upload:	sabina-bishop
View:	216 times
Download:	0 times

© 2009 Pearson Education Canada 3/1 Chapter 3 Demand Theory.

Documents