# Price demand curves and income elasticity

1) In order to attract more customers on Mondays (A slow day), Alex's Pizza Shop in Austin decided to reduce the price of their pizza rolls from $3.50 to $2.50. As a result, Monday sales increased from 70 to 130. Also, Alex's sales of soft drinks rose from 40 to 90.

a. Calculate the arc price elasticity of demand for the pizza rolls.

b. Calculate the arc cross-price elasticity of demand between soft drink sales and pizza rolls prices.

2) The demand curve for product X is given as Q = 20000 - 20P

a. How many units will be sold at $10?

b. At what price would 2,000 units be sold? 0 units? 1,500?

c. What will be the total revenue at a price of $70? What will be the marginal revenue?

d. What is the pint elasticity at a price of $70?

3) Manning's Inc. is the leading manufacturer of garage doors. Demand for residential garage door sales depends, of course, on the rate of new house building activity. The garage doors sell at an average price of $1,500 per door. In the coming year, disposable income per capita is expected to increase from $32,000 to $34,000. Without any price change Manning expects current-year sales to rise to 12,000 units.

a. Calculate the arc income elasticity of demand.

b. The company economist estimates that if the price of doors is increased by $100, they could sell 11,500 doors. What is the arc price elasticity and what would be the company's revenue?

c. Should they raise the price even more?

4) The Compute Company store has been selling its special word processing software, ACEWORD, during the last 10 months. Monthly sales and the price for Aceword are shown in the following table. Also shown are the prices for a competitive software, Goodwrite, and estimates of monthly family income. Calculate the appropriate elasticity's keeping in mind that you can calculate elasticity measure only when all other factors do not change.

MONTH PRICE QUANTITY FAMILY PRICE

ACEWORD ACEWORD INCOME GOODWRITE

1 $120 200 $4,000 $130

2 $120 210 $4,000 $145

3 $120 220 $4,200 $145

4 $110 240 $4,200 $145

5 $114 230 $4,200 $145

6 $115 215 $4,200 $125

7 $115 220 $4,400 $125

8 $105 230 $4,400 $125

9 $105 235 $4,600 $125

10 $105 220 $4,600 $115

5) The ABC Company manufactures AM/FM clock radios and sells on average 3,000 units monthly at $25 each to retail stores. Its closest competitor produces a similar type of radio that sells for $28.

a. If the demand for ABC's product has an elasticity coefficient of -3, how many will it sell per month if the price is lowered to $22?

b. The competitor decreases its price to $24. If cross-elasticity between the two radios is 0.3 what will ABC's monthly sales be?

6) Mr. Smith has the following demand equation for a certain product:

Q = 30 - 2P

a. At a price of $7, what is the point elasticity?

b. Between prices of $5 and $6, what is the arc elasticity?

c. If the market is made up of 100 individuals with demand curves identical to Mr. Smith's, what will be the point and arc elasticity for the conditions specified in parts a and b?

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#### Solution Preview

1) In order to attract more customers on Mondays (A slow day), Alex's Pizza Shop in Austin decided to reduce the price of their pizza rolls from $3.50 to $2.50. As a result, Monday sales increased from 70 to 130. Also, Alex's sales of soft drinks rose from 40 to 90.

a. Calculate the arc price elasticity of demand for the pizza rolls.

Arc price elasticity of demand for the pizza rolls = (Q2-Q1)/(Q2+Q1)*(P2+P1)/(P2-P1)

= (130-70)/(130+70)*(2.50+3.50)/(2.50-3.50) = -1.80

b. Calculate the arc cross-price elasticity of demand between soft drink sales and pizza rolls prices.

Arc cross-price elasticity of demand between soft drink sales and pizza rolls prices = (Q2y-Q1y)/(Q2y+Q1y)*(P2x+P1x)/(P2x-P1x)

= (90-40)/(90+40)*(2.50+3.50)/(2.50-3.50) = -2.31

2) The demand curve for product X is given as Q = 20000 - 20P

a. How many units will be sold at $10?

Q = 20000 - 20*10 = 19,800

b. At what price would 2,000 units be sold? 0 units? 1,500?

Writing the reverse demand equation P = (20000-Q)/20 = 1000-0.05Q

For Q = 2000, we have P = 1000 - 0.05*2000 = $900

For Q = 0, we have P = 1000 - 0.05*0 = $1,000

For Q = 1500, we have P = 1000 - 0.05*1500 = $925

c. What will be the total revenue at a price of $70? What will be the marginal revenue?

First calculate the quantity sold at P = $70

Q = 20000 - 20*70 = 18,600

TR = P*Q = 18600*70 = $1,302,000

For MR, first write the equation for TR

TR = P*Q = (1000 - 0.05Q)*Q

MR = dTR/dQ = 1000 - 0.1Q

At P = 70, Q = 18,600

MR = 1000 - 0.1*18600 = -860

d. What is the point elasticity at a price of $70?

Point price elasticity = dQ/dP = -20

The point price elasticity is constant at -20.

3) Manning's Inc. is the leading manufacturer of garage doors. Demand for residential garage door sales depends, of course, on the rate of new house building activity. The garage doors sell ...

#### Solution Summary

The solution discusses the price demand curves and income elasticity.