Demand and ElasticitiesMicroeconomic Analysis

1-808-07

Tuesday September 8th 2009

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Recap

jbgrou@umich.edu (subject: “HEC”)

Office hoursMonday 14:00 -15:00Tuesday 15:30 – 16:30

First Quiz: Tuesday Sept 22nd

HWs: see syllabus for suggested exercises

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In-class survey

Reason for choosing HEC: Top school, good reputation

Trilingual program

Cheap

International student body

Background in EconomicsNone

French Bacc

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In-class survey

Grade objective: Average answer A

10 years from now: CEO Travel Sustainable development Intl organisation HR Consulting My own firm

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In-class survey

Interesting about you:Many different origins (France, Columbia, Tahiti,

etc.)Small business ownerSkydiverDrum playerTouched a sharkSpeaks four languages…

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Today

Review of last week

Demand

From MV(q) to qid(p)

Elasticities

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So far…

ValuationV(q) vs. MV(q)Buyer’s decision: P ≤ MV(q)Seller’s decision: MC(q) ≤ P

Gains from trade Surplus

Efficiency / Pareto OptimalityMC(q) = MV(q)

DemandDemand

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Goals

To go from the behavior of individuals to that of an entire population

To analyze the determining factors of an economy

Being able to understand and to react appropriately to various economic circumstances

p

Q

D

Individual demand

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Recall: marginal valuation

q

1

2

3

4

Price

0 5 10

MV(q)

0 4

2,5 3

5 2

7,5 1

10 0

Quantity Marginal ValuationMV(q)

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Recall: marginal valuation

0 4

2,5 3

5 2

7,5 1

10 0

q

How many units would this person buy for a price of $2.50?

MV(q) P < MV(q)?

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Recall: marginal valuation

0 4 Yes Buy!

2,5 3 Yes Buy!

5 2 No Stop!

7,5 1 No

10 0 No

q

How many units would this person buy for a price of $2.50?

MV(q) P < MV(q)?

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From MV(q) to qid(p)

For each price, correspond a quantity demanded by the consumer.

In the previous example, a price of $2.50 corresponds to a demand of 2 units.

expenses

Consumer behaviorAt a given unit price, the consumer will choose the quantity, q, which maximizes her surplus: MV(q) = P.

q

1

P = 2

3

4

Prix

0q = 5 10

MV(q)

surplus

Valuation and individual demand

MV(q) = P : the consumer’s demand curve coincides with her marginal valuation curve.

q

1

P = 2

3

4

Price

0q = 5 10

d = MV

Market demand

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Market demand

The aggregate demand of an entire population.

Market quantity demanded is the sum of quantities demanded by all individuals:

i

di

d qQ

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Market demand

0 10 __

1 7,5 __

2 5 __

3 2,5 __

4 0 __

Price Ind. quantity Market (4 identical consumers)($) (q) (Q = 4xq)

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Market demand

0 10 40

1 7,5 30

2 5 20

3 2,5 10

4 0 0

Price Ind. quantity Market (4 identical consumers)($) (q) (Q = 4xq)

Market demand

1

2

3

4

Price

0

5

5 10 15 20 25 30

Draw the demand curve of a population made up of 4 consumers with individual market demand, d.

d

The market demand curve is the horizontal sum of individual demand curves…

4035

Quantitydemanded

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Market demand

Quantitydemanded 1

2

3

4

Price

0

5

5 10 15 20 25 30

d

The market demand curve is the horizontal sum of individual demand curves…

4035

D

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The demand function

Demand for Coca-Cola (undiluted syrup):

Qd = 26.17 - 3.98 Pc + 2.25 Pp + 2.60 Ac – 0.62 Ap + 9.58 S + 0.99

Y

With: Qd = quantity demanded of Coca-Cola syrup

Pc, Pp = prices of Coca-Cola and Pepsi syrups

Ac, Ap = advertisement expenditures of Coca-Cola and Pepsi

S = seasonal indicator (=1 if spring or summer, =0 otherwise)

Y = household income

Factors affecting demandQuantity demanded, Qd, generally depends on… :

…the price of the good (falls when the price rises)

…the price of other goods, Po: If Po ↑ Qd ↑, the goods are substitutes If Po ↑ Qd ↓, the goods are complements

… household income: If Y ↑ Qd ↑, the good is normal If Y ↑ Qd ↓, the good is inferior

…other factors. (Examples?)

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Factors affecting demandQuantity demanded, Qd, generally depends on… :

Giffen goods

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Exercise

Consider the demand for minivans in the U.S.:

Qd = 12 – 0,6 P + 0,2 Ps – 3 Pg + 0,2 Y

With: Qd = qty demanded (in hundreds of thousands)

P = price of a minivan (in thousand $)

Ps = price of a station wagon (in thousand $)

Pg = price of gasoline (in $ per gallon)

Y = household income (in thousand $ per year)

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Exercise (cont.)

A. Draw the demand curve for

Ps = $16,000, Pg = $3/gal, and Y = $25,000/yr.

P

Qd

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Exercise (cont.)

B. Are minivans a normal good?

They can be a normal good over a certain range of income (lower) and become an inferior after a certain range (higher), where rich people would substitute away from minivan once they start getting wealthy enough.

C. Are minivans and station wagons substitutes or complements?

D. Are minivans and gasoline substitutes or complements?

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Exercise (end)

Effect of a fall in income (crisis):

Effect of an increase in the price of station wagons:

P

Qd

D

P

Qd

D

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Exercise (end)

Effect of a fall in income (crisis):

Effect of an increase in the price of station wagons:

P

Qd

D

P

Qd

D

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Summary

A change in the price of a good leads to a movement along the demand curve for that good.

A change in a factor other than the price of the good leads to a shift of the demand curve.

Elasticities

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Price-elasticity of demand

Elasticity : A number representing the sensitivity of one variable (e.g., Qd) to changes in another variable (e.g., P).

Interpretation: The price-elasticity of demand is the percentage change in Qd when P changes by 1%.

% change in Qd ∆Qd/Qd

Ep = --------------------------- = ---------------- % change in P ∆P/P

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Computation: local method

Hence, with Qd = 280 – 20P, we get ∆Qd/∆P = -20 everywhere.

At P = 3$, we get Qd = 220 and Ep = - 20 x 3/220 = - 0.27.

At P = 4$, we get Qd = 200 and Ep = - 20 x 4/200 = - 0.4.

Note: The value of the elasticity of demand depends on where we are on the demand curve.

dQ

P

P

QEp

d

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Ep on a linear D:

We say that D is:

Ep = - ∞: perfectly elastic

Ep = 0: perfectly inelastic

Ep = -1: unit elastic

-∞ < Ep < -1: relatively elastic

-1 < Ep < 0: relatively inelastic

P

Q

__ < Ep< __

Ep < __

Ep = __

Ep= ___

Ep = __

dQ

PconstEp .

D

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Special cases

Ep = ____

Examples?

P

Qd

D

Ep = ____

Examples?

P

Qd

D

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Special cases

Ep = 0

Examples?

Drug

P

Qd

D

Ep = ∞

Examples?

Bottled water

P

Qd

D

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Ep and producer revenue

R = p x Qd A price increase does not necessary lead to an increase in revenue.

Hence, the percentage change in revenue in response to a 1% change in price is:

Question: When is it profitable for a producer to raise prices?

% change in R ∆R/R----------------------------- = ---------------- = … = 1+Ep

% change in p ∆p/p

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Ep and producer revenue

Graphically

Rectangles vs. squares

Concave revenue graphs

Maximizing a concave function

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Other elasticities (1)

The income elasticity of demand is the relative change in Qd in response to a 1% change in income (Y).

If EY > 0, we say the good is ____________,

If EY < 0, the good is ______________.

Examples?

% change in Qd ∆Qd/Qd

EY = ------------------------- = ---------------- % change in Y ∆Y/Y

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Other elasticities (1)

The income elasticity of demand is the relative change in Qd in response to a 1% change in income (Y).

If EY > 0, we say the good is normal

If EY < 0, the good is inferior.

Examples?

% change in Qd ∆Qd/Qd

EY = ------------------------- = ---------------- % change in Y ∆Y/Y

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Other elasticities (2)

The cross-price elasticity is the percentage change in Qd of a good X in response to a 1% change in the price of another good, PY.

If EcXY < 0, the goods X and Y are ________________.

If EcXY > 0, they are ____________________________.

Examples?

% change in QdX ∆Qd

X /Qd

X

EcXY = ----------------------- = ---------------- % change in PY ∆PY/PY

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Other elasticities (2)

The cross-price elasticity is the percentage change in Qd of a good X in response to a 1% change in the price of another good, PY.

If EcXY < 0, the goods X and Y are Substitutes

If EcXY > 0, they are Complements

Examples?

% change in QdX ∆Qd

X /Qd

X

EcXY = ----------------------- = ---------------- % change in PY ∆PY/PY

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Conclusion

We now know:

How to derive the purchasing behavior of an individual and of a population

How demand is affected by economic circumstance

How to predict changes and react accordingly