The inverse demand curve for a product using resource X is given by P = 200-0.5Q and the cost of production is constant at MC = 25.

a. Find the static equilibrium for this product in a single time period (call thist₀) (recall at equilibrium Supply equates Demand and in this case Demand or Price = Marginal Cost).

b. What is the value of consumer surplus from consumption in t₀? (recall, this is simply the area under the demand curve and above the price, which now equates Marginal Cost)

Imagine that resource X is infinite in supply or perfectly renewable and that the demand and supply curves are unchanged between years.

c. How much would be produced/consumed in the following year (called t₁)?

Because Marginal Cost is constant in this example, it is possible to simply subtract MC from the demand curve to establish the Net Marginal Benefits (i.e. the Consumer Surplus) in each time period. This effectively creates a Net Marginal Benefit curve that shifts downwards from the initial demand curve but remains parallel.

Thus, the Net Marginal Benefits are given by NMB = 200 - 0.5Q - 25 = 175 - 0.5Q

Now imagine that there is not enough of resource X to support the static efficient consumption in both time periods (i.e. t₀ and t₁). More specifically, assume that the total stock available in both periods is 600 units.

d. How much is consumed in t₀?

e. How much is left to consume in t₁?

You may find this distribution is quite uneven with most consumption occurring in t₀.

f. Assume a discount rate of 8%, how much is the NMB of the following year (period t₁)? (note that you need to discount the future value of NMB in period t₁ into a present value).Hint: take the NMB formulae for t₁- assumed the same as for t₀ - and divide by the factor 1.08 (because the discount rate is 8%).