# rev3 - Capital 1. Suppose a winery is a profit-maximizing...

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Capital 1. Suppose a winery is a profit-maximizing firm and is considering when to sell a new wine. The value of the wine increases as it ages, and the value of the wine in year t is f(t)=exp(0.18t-0.0025t 2 ). Assume that the real rate of interest is 7 percent. (Hint: Remember from calculus that de x /dx = e x .) a) Explain in words and mathematically when the firm will sell the wine. b) Explain how an increase in the real interest rate to 10 percent would affect the firm’s marketing strategy c) The owners of the winery decide to store the wine until the value of the wine is maximized. How long will they store the wine? Discuss whether this strategy is in the owner’s best economic interests. Answer: a) The company will let the wine age until the proportional rate of growth in the value of the wine equals the interest rate, i.e., r=f’(t)/f(t). If r=.07 then t=22. b) If the interest rate rises, then the firm will sell the wine sooner and invest the money at the market rate of interest. They will not accept a proportional rate of growth in the value of the wine that is less than 0.1, since they can sell the wine and earn a market rate of return on their profits. Therefore, the company will sell the wine, when the wine is appreciating more rapidly than in part a. If r=.10 then t=16. d) The value of the wine is a maximum when t=36. This strategy is not wise unless the real rate of interest is zero. Extra aging does not increase the value of the wine very rapidly as we approach t=36, so the firm is better off selling the wine and putting its earnings in the bank or some other investment earning r. 2. Treetop Corporation is a profit-maximizing forestry company. The firm plants trees and harvests the trees for lumber. The firm owns a grove of trees that appreciates over time. The value of the grove in year t is f(t)=exp(0.16t-0.0032t 2 ). Assume that the real rate of interest is 0.064. (Hint: Remember from calculus that de x /dx = e x .) a) Explain in words and mathematically when Treetop should cut the trees in the grove. b) Explain how an increase in the real interest rate to 0.08 would affect the firm’s tree harvesting strategy. c) An environmental group attacks Treetop’s harvest policy. The group would prefer that the trees not be cut and encourages Treetop to at least let the trees grow to full maturity (i.e., until they stop growing). When will the value of the grove reach its maximum level? Explain whether Treetop will wait for the trees to fully mature (consider profit maximizing strategies if the interest rate changes). Answer: a) The company will let the trees grow until the proportional rate of growth in the value of the wine equals the interest rate, i.e., r=f’(t)/f(t). If r=.064 then t=15. b)

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## This note was uploaded on 05/06/2010 for the course ECON econ 101 taught by Professor Buddin during the Spring '10 term at UCLA.

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rev3 - Capital 1. Suppose a winery is a profit-maximizing...

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