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Elasticity (16 problems)


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Problem #1: General Elasticity Problems

A typical consumer behaved in the following manner with respect to purchases of butter over the past eight years:

Year

Price of Butter

($/pound)

Quantity of Butter Purchased

Real Income

($)

Price of Margarine

($/pound)

1

0.95

200

11000

0.65

2

1.1

180

11000

0.65

3

1.1

190

11500

0.65

4

1.1

200

11500

0.9

5

1.15

170

11500

0.9

6

0.99

190

11500

0.9

7

0.99

175

10500

0.9

8

0.99

150

10500

0.65

Compute all meaningful price, income and cross-elasticity coefficients. (Remember that the effects of the other factors need to be held constant when computing any of these coefficients).

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Problem #2: General Elasticity Problems

Between 1999 and 2000, the quantity of automobiles produced and sold declined by 20 percent. During this period, the real price of cars increased by 5 percent, real income levels declined by 2 percent, and the cost of gasoline increased by 20 percent. Knowing that the income elasticity of demand is +1.5 and the cross price elasticity of gasoline and cars is -0.3.

a) Compute the impact of the decline in real income levels on the demand for cars

b) Compute the impact of the gasoline price increase on the demand for cars.

c) Compute the price elasticity of the demand for cars during this period.

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Problem #3: General Elasticity Problems

A number of empirical studies of automobile demand have been made yielding the following estimates

Study

Income Elasticity

Price Elasticity

Chow

3

-1.2

Alkinson

2.5

-1.4

Roos and Von Szeliski

2.5

-1.5

Suits (as reworked)

3.9

-1.2

Assume that income and prices effects on automobile sales are independent and additive. Assume also that the auto companies intend to increase the average price of an automobile by 6 hours in the next year and the next year’s disposable personal income is expected to be4% higher than this year’s. If this year’s automobile sales were 11 million units, how many would you expect to be sold under each pair of price and income demand elasticity estimates?

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Problem #4: General Elasticity Problems

Briefly answer the following

a) Why is the price of a natural resource eg. land perfectly inelastic?

b) Why does a baseball player earn a larger income than does a switchboard operator?

c) What is the distinction between an economic rent and opportunity cost?

d) Is the income that the Toronto Maple Leafs pays its players an economic rent or an opportunity cost?

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Problem #5: General Elasticity Problems

a) Suppose the cross elasticity of demand for products X and Y is +4.6 and for products E and F is -6.2. What can you conclude about the relationship of products X and Y of E and F?

b) The income elasticities of demand for movies, dental services, and clothing have been estimated to be +3.4, +1.0, and 0.5 respectively. Interpret these coefficients. What does it mean if an income elasticity coefficient is negative?

c) Mark's income has increases from $20,000 to $25,000. His sister has observed that his demand for Caribbean vacations has increased by 12% while his demand for McDonalds lunches has decreased by 8%. Calculate Mark's income elasticity of demand for

(i) vacations to the Caribbean, (ii) McDonalds lunches

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Problem #6: General Elasticity Problems

Suppose the demand function is Q xd = 100 - 8Px + 6Py - M. I\f Px = $4, Py = $2, and M = $10, what is the cross-price elasticity of good x with respect to the price of good y?

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Problem #7: General Elasticity Problems

A typical consumer behaved in the following manner with respect to purchases of butter over the past eight years:

Year

Price of Butter

($/pound)

Quantity of Butter Purchased

Real Income

($)

Price of Margarine

($/pound)

1

0.95

200

11000

0.65

2

1.1

180

11000

0.65

3

1.1

190

11500

0.65

4

1.1

200

11500

0.9

5

1.15

170

11500

0.9

6

0.99

190

11500

0.9

7

0.99

175

10500

0.9

8

0.99

150

10500

0.65

Compute all meaningful price, income and cross-elasticity coefficients. (Remember that the effects of the other factors need to be held constant when computing any of these coefficients).

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Problem #8: General Elasticity Problems

Between 1999 and 2000, the quantity of automobiles produced and sold declined by 20 percent. During this period, the real price of cars increased by 5 percent, real income levels declined by 2 percent, and the cost of gasoline increased by 20 percent. Knowing that the income elasticity of demand is +1.5 and the cross price elasticity of gasoline and cars is -0.3.

a) Compute the impact of the decline in real income levels on the demand for cars

b) Compute the impact of the gasoline price increase on the demand for cars.

c) Compute the price elasticity of the demand for cars during this period.

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Problem #9: General Elasticity Problems

a) Suppose the cross elasticity of demand for products X and Y is +4.6 and for products E and F is -6.2. What can you conclude about the relationship of products X and Y of E and F?

b) The income elasticities of demand for movies, dental services, and clothing have been estimated to be +3.4, +1.0, and 0.5 respectively. Interpret these coefficients. What does it mean if an income elasticity coefficient is negative?

c) Mark's income has increases from $20,000 to $25,000. His sister has observed that his demand for Caribbean vacations has increased by 12% while his demand for McDonalds lunches has decreased by 8%. Calculate Mark's income elasticity of demand for

(i) vacations to the Caribbean, (ii) McDonalds lunches

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Problem #10: General Elasticity Problems

How would the following changes in price affect total revenue? That is would total revenue increase, decline, or remain unchanged

a) Price rises and demand is inelastic

b) Price falls and demand is elastic.

c) Price rises and supply is elastic

d) Price falls and demand is unit elastic

e) Price falls and demand is inelastic

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Problem #11: Income Elasticity of Demand

You are the manager of a supermarket, and know that the income elasticity of peanut butter

is exactly -0.7. Due to the recession, you expect incomes to drop by 15% next year.

How should you adjust your purchase of peanut butter?

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Problem #12: Own Elasticity of Demand

Suppose Q xd = 10,000 - 2 Px + 3 Py - 4.5M , where Px = $100, Py = $50, and M = $2,000. What is the own-price elasticity of demand?

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Problem #13: Own Elasticity of Demand

You are told that the price elasticity of demand at the current equilibrium in the WTI crude oil market (P = $84 per barrel and Q = 252 million barrels per day1) is equal to -2.

a) Derive a linear demand function satisfying the properties above. Illustrate this function on a graph with Q on the x-axis and P on the y-axis.

b) What is your estimate of the choke price?

c) What would have happened to your estimate of the slope and the choke price, had the demand been less elastic at the current equilibrium? Illustrate your answer on a graph.

d)Had the market demand been greater than 252 at the current P and with the same price elasticity of demand, what would have happened to your estimate of the slope of demand? Can you unambiguously predict the effect on the choke price? Illustrate your answer on a graph.

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Problem #14: Own Elasticity of Demand

If a price increase from $5 to $7 causes quantity demanded to fall from 150 to 100, what is the absolute value of the own-price elasticity at a price of $7?

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Problem #15: Own Elasticity of Demand

Suppose that the current market price of VCR’s is $300, the average consumer has disposable income of $30,000 and the price of laser disk players (a substitute for VCR's) is $500. Under these conditions the annual US demand for VCR's is 5 million per year. Statistical studies have shown that for this product the own price elasticity of demand is , the income elasticity of demand isand the cross price elasticity of demand is, where P' is the price of laser disk players. Use this information to predict the annual number of VCR's demanded (forget about the supply) under the following conditions:

a) Increasing competition from Korea causes VCR prices to fall to $270 with I and P' unchanged.

b) Income and tax reductions raise average disposable income to $31,500 with P and P' unchanged.

c) Technical improvements in laser disk players cause their price to fall to $400 with P and I unchanged.

d) All the events above simultaneously.

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Problem #16: Own Elasticity of Demand
Define: Price Elasticity: Cross Price Elasticity and income elasticity. Why are they important?
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