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. In the numerical example given in lecture, the inverse demand function for the depletable resource is P = 8 – 0.4q and the marginal cost of supplying it is $2.
   1. If 20 units are to be allocated between two periods, in a dynamic efficient allocation how much would be allocated to the first period and how much to the second period when the discount rate is zero? (Show work)
   2. What would the efficient price be in the two periods?
   3. What would the marginal user cost be in each period?

Answer 1

2o 23

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.