4.A fixed amount of a mineral (Q) is available for consumption in period 1 (q₁) and/or period 2 (q₂). The demand functions for the mineral in each period are the same and are given by and where and are the prices for the mineral in each period. Assume that the marginal extraction cost is zero.

a.Calculate the equilibrium price and quantity in each period if Q = 180, the discount rate used by the suppliers of the mineral is 10 % per year, and the suppliers of the mineral behave competitively (i.e. they are price takers).

b.Calculate the equilibrium price and quantity in each period if Q = 180, the discount rate used by the suppliers of the mineral is 20% per year, and the suppliers of the mineralbehave competitively (are price takers).

c.How would an increase in the interest rate to 20% in (b) affect your answer and why?

d.Calculate the equilibrium price and quantity in each period if Q = 180, the mineral supplier is a monopoly who owns the entire resource and uses a discount rate of 10% per year.