The following information represents the demand, cost, and resource stock relationships for a non-renewable energy resource:

Demand: Pt = 15 - qt

Supply: MCt = 3 - .1qt

Discount rate: r = .05

Energy resource stock: q0 + q1 = 20

Where:

Pt = price in time period t (0 or 1)

qt = quantity produced in time period t (0 or 1)

MCt = marginal cost in designated time period

r = discount rate

1.Assuming the resource is extracted in two time periods, the present (this year) and the future (next year), what are the optimal quantities of energy resource (q0 and q1) used in time period t=0 and time t=1 and prices p0 and p1 in a perfectly competitive and perfectly functioning market? At what rates do rents increase from time period t=0 to t=1 in the competitive market?

2.What would be the quantities q0 and q1 and prices p0 and p1 in a monopolistic market?

3.Assume that the marginal cost of production next year changes to MC(next year) = 4 - .1qt . What are the optimal quantities of energy resource (q0 and q1) used in time period t=0 and time t=1 and prices p0 and p1 in a perfectly competitive and perfectly functioning market? At what rates do rents increase from time period t=0 to t=1 in the competitive market?

4.Suppose that we want to delay extraction of the energy resource into the future. What government policy could be implemented to help achieve this goal?