Question

Suppose there are 500 tons of neodymium, a valuable rare-earth metal, in a given mine. The entire
500 tons are to be mined in 2 years by a competitive mining sector. They discount future returns at
10% (so we have r = :1 or d = 1:1) and the marginal cost of mining is $0 per ton. Inverse demand for
neodymium is given by P = 200 ? Q=2 in each period.
a. If half of the neodymium (250 tons) is mined in each period, for each period determine the price
at which neodymium will be sold. What is net revenue (or prot) in each period? What is the
present value of net revenue across both periods?

Answer 1

In this case P=200-Q/2

MC=0

a)

Set Q=250 in first period

P1=200-(250/2)=$75

Total Profit in period 1==Net Revenue in period 1=P1*Q1=75*250=$18750

Extraction in period 2=q2=500-250=250

P2=200-(250/2)=$75

Total Profit in period 2==Net Revenue in period 2=P2*Q2=75*250=$18750

Present value of net revenue in period 1==$18750

Present value of net revenue in period 2=/(1+r)=18750/(1+0.10)=$17045.45

Total PV=18750+17045.45=$35795.45