CDAE 254 - Class 14 Oct. 12

Last class:4. Market demand and elasticity

Today:4. Market demand and elasticity5. ProductionQuiz 4 (sections 3.4 – 3.7 and 4.1-4.5)

Next class:5. ProductionReview for the midterm exam

Important dates:Problem set 4 due Tuesday, Oct. 17Midterm exam (Chapters 1-4): Thursday, Oct. 19

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

4.3. 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 PercentageQin change Percentage

, PQe

QP

PQ

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 = -0.25Conclusion: Price elasticity of demand changes from one point to another point on the same demand curve.

QP

PQe PQ

, QP

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 PercentageQin change Percentage

, IQe

QI

IQ

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

QP

PQ

j

j

i

i

PP

QQ

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 (Thursday, Oct. 12)

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)