CDAE 254 - Class 13 Oct. 10

Last class:3. Individual demand curves4. Market demand and elasticity

Today:4. Market demand and elasticity

Next class:4. Market demand and elasticity5. ProductionQuiz 4 (Sections 3.4 – 3.7 and 4.1 – 4.5)

Important dates:Problem set 3 due todayProblem set 4 due Tuesday, Oct. 17Midterm exam (Chapters 1-4):

Problem set 4

-- Please use graphical paper to draw graphs

-- Please staple all pages together before you turn them in

-- Scores on problem sets that do not meet the above requirements will be discounted.

Six problems:4.1., 4.2., 4.4., 4.6., 4.7., and 4.8

3. Individual demand curves3.1. Basic concepts

3.2. Demand functions

3.3. Changes in income

3.4. Changes in a good’s price

3.5. Changes in the price of another good

3.6. Construction of individual demand curves

3.7. Consumer surplus

3.8. Applications

3.7. Consumer surplus and welfare analysis (1) What is consumer surplus (CS)?

The extra value individuals receive from consuming a particular amount of a good over what they pay for that.

CS = Amount of willingness to pay – actual cost

(2) A graphical analysis (Fig. 3.10)

(3) Change in CS

(4) Applications

Class Exercise (Thursday, Oct. 5)

For demand function Q = 28 - 2P,

(a) What is the consumer surplus when the price (P) is equal to $6 per unit?

(b) What is the change in consumer surplus when a sales tax of $1 per unit is added to the current price of

$6 per unit?

3.8. Applications (1) Income tax vs sales tax

(2) Income subsidy vs. price subsidy(3) Change in consumer surplus – a measure of

the impacts on consumer welfare due to change in price

4. Market demand and elasticity

4.1. Market demand curves

4.2. A general definition of elasticity

4.3. Price elasticity of demand

4.4. Income elasticity of demand

4.5. Cross-price elasticity of demand

4.6. Empirical studies of demand

4.7. Applications

4.1. Market demand curves (1) Basic concepts

Market demand: Market demand curve:(2) Construction of a market demand curve(3) General notations regarding a market:(4) Shifts in the market demand curve -- A change in individuals’ income -- A change in population -- A change in the price of another good ……

4.2. A general definition of elasticity (1) How to measure the response of demand to

a change price?

(2) Definition of elasticity:

The percentage change in one variable (Y) brought about by a 1% change in another variable (X).

(3) A mathematical notation:

Elasticity of Y with respect to X

= Xin change Percentage

Yin change Percentage

4.2. A general definition of elasticity (4) How to calculate a percentage change?

e.g., If X increased from 10 to 12, what is the percentage change in X?

Percentage change in X

If X decreased from 12 to 10, what is the percentage change in X?

change thebefore X of Value

Xin change

%202.010

10-12

X

X

4.2. A general definition of elasticity (5) How to calculate an elasticity?

e.g., when X increased from 10 to 12, Y increased from 100 to 110, what is the

elasticity of Y with respect to X?

Elasticity of Y with respect to X

eY, X =

= Xin change Percentage

Yin change Percentage

5.020%

10%

4.3. Price elasticity of demand (1) What is price elasticity of demand?

-- Definition: The percentage change in the

quantity demanded of a good in response to a

1 percent change in its price.

-- Mathematical definition:

Pin change Percentage

Qin change Percentage, PQe

Q

P

P

Q

PP

QQ

Class Exercise (Thursday, Oct. 5)

1. Mr. Smith’s demand for hair cut decreased from 10 times per year to 8 times per year when the price increased from $15 to $18, what is his demand elasticity of price for hair cut?

2. For demand function Q = 28 - 2P, what is demand elasticity of price when P = 8?

4.3. Price elasticity of demand (2) Factors that affect price elasticity of demand:

-- Possibility of substitution

-- Time of adjustment

……

(3) Range of price elasticity of demand:

< -1 elastic (e.g., -1.5)

= -1 unit elastic

> -1 inelastic (e.g., -0.6)

4.3. Price elasticity of demand (4) How to calculate price elasticity of demand?

(a) When we have two observations on Q and P:

e.g., Q decreased from 100 to 80 when P

increased from $10 to $11 per unit, what

is the price elasticity of demand?

4.3. Price elasticity of demand (4) How to calculate price elasticity of demand?

(b) When we have a demand function:

e.g., P = 50 - 0.5 Q or Q = 100 - 2 P

when P = 40, Q = 20, eQ,P = -4

when P = 25, Q = 50, eQ,P = -1

when P = 10, Q = 80, eQ,P = -0.25

Conclusion: Price elasticity of demand changes from one point to another point on the same demand curve.

Q

P

P

Qe PQ

, Q

P 2

4.3. Price elasticity of demand (5) Relation between TR and price elasticity

(a) TR and market share

(b) Relation between market share or TR and eQ, P -- How to calculate market share of each company?

-- When the demand is elastic (e.g., eQ, P = -2):

↑ P TR = P*Q

↓ P TR = P*Q

-- When the demand is inelastic (e.g., eQ, P = -0.6):

↑ P TR = P*Q

↓ P TR = P*Q

-- When the demand is unit elastic (i.e., eQ, P = -1):

Class exercise(Tuesday, Oct. 10)

When the price of U.S. cigarettes increased from 20 to 24 in the Chinese market, the demand for U.S. cigarettes decreased from 100 to 90 units.

(a) What is the price elasticity of demand for U.S.

cigarettes in China?

(b) If the U.S. wants to increase its market

share in the Chinese cigarette market,

should the U.S. cigarette price in China

be increased or decreased?

4.4. Income elasticity of demand (1) What is income elasticity of demand?

The percentage change in the quantity

demanded of a good (Q) in response to a 1%

change in income.

Iin change Percentage

Qin change Percentage, IQe

Q

I

I

Q

II

QQ

4.4. Income elasticity of demand (2) Range of income elasticity of demand:

< 0 inferior good

< 1 inelastic

= 1 unit elastic

> 1 elastic

(3) An example:

When the average monthly income increased

from $2000 to $2200, printer demand increased

from 100 to 125. What is the income elasticity of demand for printer?

4.4. Income elasticity of demand (3) Another example:

Q = 200 + 0.005 I - 0.02 P

where Q = demand for computer

I = average income

P = average price

What is the income elasticity of demand when the average income is $30,000 and the average computer price is $1,500?

4.6. Cross-price elasticity of demand

(1) Definition: The percentage change in the quantity demanded of a good (Q) in response to a 1% change in the price of another good.

j

i, Pin change Percentage

Qin change Percentage

ji PQe

i

j

j

i

Q

P

P

Q

j

j

i

i

P

PQQ

4.6. Cross-price elasticity of demand

(2) How to calculate cross-price elasticities?

(1) When we have two observations:

e.g., the demand for pork increased from 100 to 110 when the price of beef increased from 3 to 3.6, what is the elasticity of pork demand with respect to beef price?

(2) When we have a demand function:

e.g., Qpork = 40 - 2 Ppork + 0.5 Pbeef

What is the elasticity of pork demand with respect to beef price when the pork price is 4 and beef price is 6?

Class Exercise (Tuesday, Oct. 10)

For demand function Qc = 300 – 0.3Pc – 0.1Pp + 0.05 I , where Qc is the demand for laptop computers in a market, Pc is the average price of laptop computers, Pp is the average price of printers and I is the average income. If we know the average laptop computer price is $800, the average printer price is $100 and the average income is $20,000, calculate:

(1) the income elasticity of demand for laptop computers:

(2) the own-price elasticity of demand for laptop computers:

(3) the cross-price elasticity of demand for laptop computers with respect to the average price of printers.

4.7. Empirical studies of demand

(1) Examples of estimated demand elasticities

(2) Estimation of demand functions (regression analysis)

(3) How to estimate demand elasticity from demand equation?

(4) Elasticity matrix (e.g., demand for animal

products in urban China)

Demand elasticities in urban China

Marshallian price elasticity of good i with respect to good j

ExpenditureElasticities

MarginalBudget % Pork B & M Poultry Eggs Fish Milk

Pork 0.8327 39.14 -0.8503 -0.1305 0.0876 0.0844 -0.0130 -0.0227

B & M 0.8492 7.26 -0.7002 -0.6745 0.0907 0.2301 0.1736 0.0717

Poultry 1.4895 17.11 0.0549 0.0092 -1.3362 -0.5057 0.2939 -0.0068

Eggs 0.9858 14.00 0.2380 0.1281 -0.3448 -0.7766 -0.1902 0.0132

Fish 1.1909 19.99 -0.2067 0.0544 0.2337 -0.2000 -1.0253 -0.0629

Milk 1.2689 0.0250 -0.8070 0.2608 -0.0303 0.0281 -0.5703 -0.2884