Assume that there is a fixed supply of certain depletable resource and consider two time periods only. The total supply of the depletable resource is 40 units. The demand (marginal willingness to pay (WTP)) is decreasing in q such that:

P = 20 - 1q and MC = $8 (MC is constant)

a) What will the efficient quantities allocated for each period be assuming that the available resource is abundant?

b) However, the depletable resource is not abundant in our case. Also assume that the value of discount rate r = 0.10. Solve for the efficient quantities of q1 and q2 for period 1 and period 2 respectively. You can use the following hints below to solve for these quantities as provided in the appendix of chapter 6.

Equation 1: 20 -1q1 - 8 - = 0 ;

Equation 2: [(20-1q2 -8)/(1.10)] - = 0 and

Equation 3: q1+q2 = 40.

c) Calculate the efficient price for both periods.

d) Calculate the marginal user cost (which is given by efficient price - MC) for each period. Also comment on the marginal user cost for period 2.