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Additional resources for Microeconomic Analysis. SOLUTIONS
To make 33 units of butter, firm 2 needs 11 barrels of oil. Chapter 19. 1 See Ingersoll (1987), page 238. a Apartments will be profitable to construct as long as the present value of the stream of rents is at least as large as the cost of construction. In equations: (1 + π)p p+ ≥ c. 1+r In equilibrium, this condition must be satisfied as an equality, so that p= 1+r c. b Now the condition becomes p= 1+r c. c Draw the first period demand curve and subtract off the K rent controlled apartments to get the residual demand for new apartments.
For the firm to make a profit, x∗2 ≥ s2 . Hence we have 1/2 ≥ u2 + 1/4, or u2 ≤ 1/4. a The professor must pay s = x2 /2 to get the assistant to work x hours. Her payoff will be x − x2 /2. This is maximized where x = 1. b The TA must get his reservation utility when he chooses the optimal x. This means that s − x2 /2 = s − 1/2 = 0, so s = 1/2. c The best the professor can do is to get Mr. A to work 1 hour and have a utility of zero. Mr. A will work up to the point where he maximizes ax + b − x2 /2.
C For c < 2/3. a Let the price of oil be 1. Then the zero-profit condition implies that pg 2x − x = 0. This means that pg = 1/2. A similar argument shows that pb = 1/3. b Both utility functions are Cobb-Douglas, and each consumer has an endowment worth 10. From this we can easily calculate that xg1 = 8, xb1 = 18, xg2 = 10, xb2 = 15. c To make 18 guns, firm 1 needs 9 barrels of oil. To make 33 units of butter, firm 2 needs 11 barrels of oil. Chapter 19. 1 See Ingersoll (1987), page 238. a Apartments will be profitable to construct as long as the present value of the stream of rents is at least as large as the cost of construction.
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