Question

Consider a two-period model where inverse linear demand for a natural resource is P = 100 – Q, and supply is flat at P = MC = 1. The discount rate is 20%. Assume society is endowed with a large amount of the resource (that is, the resource endowment is not a constraint to its allocation). a) What is the static efficient allocation for period 1? b) What is the static efficient allocation for period 2? c) What is the dynamic efficient allocation path (allocation for period 1 and 2)? d) Compare your answers of parts a, b, and c, and offer brief discussion. e) Is the dynamic allocation sustainable? Explain your answer. f) Assume the interest rate decreases to 10%, do your answers to parts a), b), or c) change? Explain your answers.

Answer 1

a) To get the static efficient allocation for period 1, let us solve the demand function and supply function for equilibrium quantity. In the short run, MC function is the supply function.

P = 100 - Q (given)........... (1)

P=MC=1 (given)..............(2)

Using (1) & (2), we get,

1 = 100 + Q or Q = 99

b) The static efficient allocation for period 2, remains same at period 1 levels i.e., 99 as the resource is not scarce.

c) Dynamic efficient allocation (Peiod 1) = Static efficient allocation (Period 1) = 99 (as no discounting is required for period 1)

For perod 2, there is an increase in MC by the interest amount between the two periods (for a discounting rate of 20%, interest rate = 25%). Therefore the supply function for period 2 becomes :- P=MC = 1.25................ (3)

Solving (3) & (1), we get Q= 98.75 = Dynamic efficient allocation (Peiod 2)

d) Since the resource availability is not a constraint, the demand and supply quantities continue to decline with time (ceteris paribus).

e) The effect of discount rate or interest rate is not considered on the demand function. The demand function could also change due to factors other than prices. Similarly, the supply function in the long run is not merely dependent on MC. Subject to these conditions, the dynamic allocation is more or less sustainable.

f) With change in interest rate to 10% (not discount rate) , there is no change in answers (a) and (b). Only the Dynamic efficient allocation (Peiod 2) will change :- Q=98.90 in part (c)