# 1. If the Demand Curve Is a Linear Function of Price, Then the Price Elasticity of Demand

EC 203 PS: CH 15 FALL 2006

1. If the demand curve is a linear function of price, then the price elasticity of demand is the same at all prices. FALSE

2. The demand for tickets to a rock concert is given by D(p) = 200,000 - 10,000p, where p is the price of tickets. If the price of tickets is \$17, then the price elasticity of demand for tickets is -5.67

3. The demand function for small business computers in the United States is given by x = 200 - 10p, where x is annual sales measured in thousands of computers and p is the price of a computer measured in thousands of dollars. Japanese firms supply a big share of these computers. They measure prices in yen where 150 yen equal 1 dollar. The price of 1 computer is \$10,000. Let Eu be the price elasticity of demand at this price as calculated by US firms who measure in dollars, and let Ej be the price elasticity of demand at the same \$10,000 price but measured in yen by the Japanese firms. What are the values of Eu and Ej? -1, -1

4. At the price of \$100, tourists demand 237 airplane tickets. At the same price, business travelers demand 247. At the price \$110, tourists demand 127 tickets and business travelers demand 127. Assuming that the demand curves of business travelers and tourists are both linear over this price range, what is the price elasticity of demand at the price \$100? -4.75

5. Waters would love to have a Mercedes. His preferences for consumption in the next year are represented by a utility function U(x, y), where x = 0 if he has no Mercedes and x = 1 if he has a Mercedes for the year and where y is the amount of income he has left to spend on other stuff. If U(0, y) = the square root of y and U(1, y) = (10/9)(y5) and if Waters' income is \$50,000 a year, how much would he be willing to pay per year to have a Mercedes? \$9,500

6. Gilmour is trying to decide whether to have 0 cars, 1 car, or 2 cars. If x is the number of cars he has and y is the amount of money he has per year to spend on other stuff, Gilmour's utility function is U(x, y), where U(0, y) = y1/2, U(1, y) = (15/14)y1/2, and U(2, y) = (10/9)y1/2. Suppose that it costs \$2,000 a year to have 1 car and \$4,000 a year to have 2 cars. Gilmour finds that the right thing to do depends on his income.
a. What is his willingness to pay for 1 car if his income is M?
b. What is the lowest income at which he would have a car?
c. What is the lowest income at which he would have 2 cars?

a. His willingness to pay for 1 car is about 0.129M, where M is his income.
b. The lowest income at which she would get a car is \$15,504.
c. If we solve the equation U(1, y - 2,000) = U(2, y - 4,000), we find \$55,143. At incomes above that he prefers 2 cars; below that he would be better off to have 1 car.

7. The demand for Floyd Adjustable Beds is described by

Qc = Pc–1.40I–0.60Pm0.20A0.25, where Qc is the number of Floyd Adjustable Beds demanded, Pc is the price of a Floyd Adjustable Bed, I is per capita income, Pm is the price of a battery-powered massage pillow, and A is the advertising budget.

a. If the marginal cost of producing a Floyd Adjustable Bed is \$200, what is the profit-maximizing price?

b. Per capita income in the United States is forecast to rise by 3% next year. How will this impact Floyd’s sales?

c. The price of battery-powered massage pillows suddenly fell by 10%. How will this impact Floyd’s sales?

a. \$700.

b. Demand will decrease by 1.8%.

c. Demand will decrease by 2%.