Suppose the (inverse) demand function for a natural resource is given as follows in the two period: P₀ = 15 - Q₀ and P₁ = 15 - Q₁. Let the marginal cost of extraction be MC₀ = 5 + Q₀ and MC₁ = 5 + Q₁. Note that P = MC in each period.

a)If the resource is not scarce (say 10 or more) what would be the optimal output in each period. (5 points)

b)Show that the optimal amount in the first period will be more than that in the second period when the resource is scarce (say Q₀+Q₁=8) with a discount rate of 10%. (10 points)