Consider two-period model of exhaustible natural resources, where the inverse demand function for resource is P = 9 0.3q in each period and the marginal cost of supplying it is $0 per unit. If the total supply of the natural resource is 30 units, and the discount rate is 20% per period,

(a) in the context of this example, is this resource a scarce resource? Why yes or why not?

(b) (i) How should this resource be allocated between the two periods? (ii) What is the marginal user cost at the optimal allocation? (iii) What would the efficient price be in the two periods? Note: graphs are essential to this problem.

4. Suppose the demand for a product is P = 100 (1/2)Q and the supply of virgin material is 150 units. The marginal cost curve for recycled material inputs is r = Q/3.

(a) Compute the socially efficient output level. In your graph, explain and indicate the quantity of recycled inputs, calculate the recycled inputs and the efficient recycling ratio.

(b) How higher efficiency in community program that support recycling change the efficient recycling ratio? Support your answers in both parts with a graph.