Oregon State University Department of Applied Economics AEC 351 Homework 2 The market for 10 mm refined cobalt (Co) cubes is perfectly competitive

Oregon State University

Department of Applied Economics

AEC 351

Homework 2

1. The market for 10 mm refined cobalt (Co) cubes is perfectly competitive. Market inverse demand is given by

   

   , where price is measured in dollars per cube and

   

    is measured in thousands of cubes.  The marginal cost curve for a typical cube

producer is ????????_????(????) = 25 + 2????_????, with ????????_???? in dollars per cube and ????_????  in thousands of cubes.

1. 1. If there are 20 identical refined cobalt cube producers active in the market,            determine the industry supply function.

1. 2. What is the market equilibrium quantity of refined cobalt cubes produced and purchased in this market, and what is the equilibrium price per cube?

1. 3. What is the typical firm's producer surplus?

1. 4. What is consumer surplus?

2. Now consider an alternative market structure where there is only one refined cobalt cube producer. This firm acts as a profit-maximizing monopolist. Assume that the monopolist’s marginal cost curve is ????????(????) = 25 + 0.1????, where

   

    is measured in thousands of cubes. Market demand for cobalt cubes is once again 

. The monopolist’s marginal revenue is

1. 1. What is the market equilibrium quantity of refined cobalt cubes sold by the monopolist, and what is price per cube charged?

1. 2. At this output level, what is the monopolist’s producer surplus?

1. 3. What is consumer surplus?

3. In complete sentences, compare and interpret your answers to Problems 1.d and 2.c.

1 of 2

4. Suppose that it is your intention to live the life of a philosopher-hermit soon after graduation from Oregon State University. You believe that the meaning of life, the universe, and everything may be found after spending three years in secluded contemplation in the wilderness. It turns out, though, that even hermits have cash flow problems. Securing supplies and rent for the appropriate cottage in which to live the life of the mind will cost $8,000 per year. Assume that you plan on residing at the cottage for three years, beginning five years from now. To pay for your philosophizing, how much money would you need to invest now if you can earn 4% on your investment? What about 9%?

5. Solve for the missing data:

Note that if:

then:

????_???? = ????????(????_????)(1 + ????)^????

or