Download Problem Set 1

Problem Set 1
Econ 613(01) Spring 2003
(Dr. Tin-Chun Lin)
1. The Johnson Robert Company’s marketing officials report to the company’s chief
executive officer that the demand curve for the company’s robots in 2001 is P =
3000-40Q, where P is the price of a robot, and Q is the number sold per month.
a. Derive the marginal revenue curve for the firm. (Answer: MR=3000-80Q)
b. At what prices is the demand for the firm’s product price elastic? (Answer: P 
$1500)
c. If the firm wants to maximize its dollar sales volume, what price should it charge?
(Answer: P = $1500)
2. Suppose: (1) the demand function of good 1 is linear, i.e. Q1  40  0.5P1 ; (2) the
demand function of good 2 is also linear; (3) the demand curve of good1 crosses the
demand curve of good2 at the P1 = $8; (4) at the point of P1 = $8, the absolute value of
price elasticity of demand 1 is ½ of the absolute value of price elasticity of demand 2.
What is the demand function of good 2? (Answer: Q2  44  P2 )
3. The Haas Corporation’s executive vise president circulates a memo to the firm’s top
management in which he argues for a reduction in the price of the firms’ product. He
says that such a price cute will increase the firm’s sales and profits.
a. The firm’s marketing manager responds with a memo pointing out that the price
elasticity of demand for the firm’s product is about -0.5. Why is this fact relevant?
(Hint: it depends on whether the demand is elastic or inelastic)
b. The firm’s president concurs with the opinion of the executive vice president. Is
he correct? (Answer: assuming that the marketing manager is correct that the
demand elasticity is -0.5, then a price reduction will cause the number of units
sold to increase by a smaller percentage than price has fallen, and both the
president and executive vice president will have egg on their faces when total
revenues decline after the price is reduced.)
4. Suppose the demand function of Y is: Qy  10665  0.5Py3  0.1Px2  0.05M
a. If Py  $10 , Px  $20 , and M = $2500, what is Ed ? (Answer: -0.15)
b. If Py  $10 , Px  $20 , and M = $2500, what is E dxy (cross elasticity of demand)?
What is the relationship between X and Y? (Answer: -0.008; complements)
c. If Py  $10 , Px  $20 , and M = $2500, what is E dI (income elasticity of demand)?
Is Y a normal good or inferior good? (Answer: -0.0125; inferior good)
5. Consider the effect of changes in fares on the quantity demanded of taxi services. Do
you expect demand to be more elastic with respect to fare changes in the short run or
the long run? (Answer: more elastic in the long run)
6. State the sign (positive or negative) and, where possible, the range (less than 1, 1,
greater than 1) of the following elasticities:
a. The elasticity of demand for ice cream at the point of maximum revenue.
(Answer: 1)
b. The cross elasticity of demand for ice cream with respect to the price of frozen
yogurt. (Answer: positive)
c. The income elasticity for Caribbean cruises. (Answer: positive)
d. The income elasticity of demand for toothpaste. (Answer: positive)
e. The elasticity of supply of Irish salmon. (Answer: positive)
f. The cross elasticity of demand for corn ready to be popped with respect to the
price of popcorn machines. (Answer: negative)