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Oregon State University Department of Applied Economics Homework 3 Consider the problem of a mining firm over two periods (0 and 1)

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Oregon State University

Department of Applied Economics

Homework 3

1. Consider the problem of a mining firm over two periods (0 and 1). The firm has access to

X  = 12 units of a nonrenewable resource and must set extraction levels in each period (q₀ and q₁, respectively). Price over the two periods is fixed at p = 20. The firm’s marginal cost of extraction is MC(q_t) = 5 + q_t.

 

1. 1. What is the firm’s total rent maximizing extraction plan assuming it applies a 10% discount rate (r = 0.1).

 

1. 2. Suppose instead X = 35. Redo Problem #1.a. Does your answer change? Provide intuition for your finding using complete sentences.

 

1. 3. Assume once again that X  = 12. What are the total resource rents the firm earns under the efficient policy in periods 0 and 1? Total resource rents in this problem are the same as the (total) profit the firm earns from mining.

               

2. Dysprocorp is a near-monopoly supplier of dysprosium. There is a competitive fringe of dysprosium producers that act as price takers of the price Dysprocorp sets. Market inverse demand for dysprosium is P^D(Q) = 400 – Q, with P measured in dollars per ton of  dysprosium and Q measured in thousands of tons of dysprosium. The fringe marginal cost curve is MC_F(q_F) = 40 + 0.5q_F (with q_F and MC_F also in thousands of tons of dysprosium and dollars per ton of dysprosium, respectively). Dysprocorp’s marginal cost of production is constant at $52 per ton. Dysprocorp needs to plan its strategy for setting the price of dysprosium.

 

[In this problem, consider a static market equilibrium in one period only and assume that the user cost of dysprosium production for both Dysprocorp and firms in the competitive fringe is zero].

 

1. 1. Determine the residual demand facing Dysprocorp after accounting for the quantity supplied by the competitive fringe.

 

1. 2. Assume that Dysprocorp’s marginal revenue after accounting for the competitive fringe is MR_r(Q_r) = 160 – (2/3)Q_r. How much dysprosium will Dysprocorp supply?

 

1. 3. What is the resulting dysprosium price?

 

1. 4. How much dysprosium is produced by the competitive fringe?