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.

b. Use Hotelling's rule to determine the optimal level of extraction, Q1 and Q2, in each period. Use the fact that, with zero extraction costs, marginal prot is simply M = P.

Answer 1

Marginal profit for each year is given as

=P1-MC=200-Q1/2-0=200-0.5*Q1

=P1-MC=200-Q2/2-0=200-0.5*Q2

We know that Q1+Q2=500

So,

Q2=500-Q1

Hence

=200-Q2/2=200-0.5*(500-Q1)=-50+0.5Q1

Hotelling rule states that

Q1=257.14 (optimal extraction in period 1)

Q2=500-257.14=242.86  (optimal extraction in period 2)