Question

Maximization of net benefits for a two period model (also profit maximization of a single owner). Two conditions must be satisfied:

            (P₂ – MC₂) = (1 + r)(P₁ – MC₁)

            q₁ + q₂ = q_total

1. Assume the same demand conditions as stated in question (1), but for this question let the discount rate r = 0.10 and the marginal cost of extraction be $4.
   1. How much would be produced in each period in an efficient allocation?
   2. What would the marginal user cost be each period?
   3. Would the static and dynamic efficiency criteria yield the same answers for this problem? Why?

Answer 1

A two period model denotes an exhaustable resource hence its supply is limited .In the figure , OP is the demand , which is constant in period 1 and period 2 because the resources are exhaustible one. It is clear from the figure that quantity q1 + q2 , where P=MC is the profitable quantity . So, OQ2 quantity is optimum level of production to maximise the profit.

2. The marginal user cost in each period must be less than marginal revenue.

3. The static and dynamic criterion will not give the same result.When the rate of interest change , if the supply is less, this will not be the optimum allocation. If supply is sufficient to meet demand then the static efficient criteria will provide the efficient allocations overtime regardless of the discount rate.In the above figure supply is sufficient hence it provides the optimum allocation of the resources.