b. If not, what would this relationship approximate?

12. Managers of the Brennan Company used regression analysis to obtain the following

estimate of the demand function for their product log Q = 2 – 1.2 log P + 1.5 log I

where Q is quantity demanded, P is price, and I is consumers’ disposable

income. a. Brennan’s president is considering a 5% price reduction. He argues

that these results indicate that such action will result in a 6% increase

in the number of units sold by the fi rm. Do you agree? Why or

why not? The firm’s treasurer calculates that the probability that the t statistic of

log P is as large (in absolute value) as it is, given that log P has no real

effect on log Q, is about 0.5. He says the estimate of the price elasticity is

unreliable. Do you agree? Why or why not?

c. How can managers obtain a more accurate estimate of the price elasticity

of demand?

 

A consulting firm specializing in agriculture determines that the following

combinations of hay and grain consumption per lamb will result in a 25-pound

gain for a lamb:

The firm’s president wants to estimate the marginal product of a pound

of grain in producing lamb. Can he do so on the basis of these data?

b. The firm’s president is convinced that constant returns to scale prevail

in lamb production. If this is true and hay and grain consumption per

lamb are the only inputs, how much gain accrues if the hay consumption

per lamb is 100 pounds and the grain consumption per lamb is 250.2

pounds? c. What is the marginal rate of technical substitution of hay for grain when

between 40 and 50 pounds of hay (and between 130.9 and 125.1 pounds

of grain) are consumed per lamb?

d. A major advance in technology occurs that allows farmers to produce a

25-pound gain per lamb with less hay and grain than the preceding table

indicates. If the marginal rate of technical substitution (at each rate of

consumption of each input) is the same after the technological advance

as before, can you draw the new isoquant corresponding to a 25-pound

gain per lamb?