Islandia is a completely isolated island that has a fixed stock of 100,000 tons of coal. Islandia will survive for two periods. Consumers in Islandia having a declining marginal benefit of coal consumption in each period. The curve is constant in real terms over time. Note: No numerical answers

(a) Assume the real interest rate in Islandia is 0%. Draw a diagram illustrating the efficient allocation of Islandia's coal stock across the two periods. Briefly explain your diagram

(b) Now assume the interest rate in Islandia is 5%. In your diagram, illustrate how the efficient allocation of Islandia's coal stock will change from your answer in (a). Explain the difference.

(c) Suppose that the stock of coal in Islandia is controlled by 10,000 individual owners, each of whom owns 10 tons of coal. Coal is purchased by a large number of individual consumers. The marginal cost of extracting and transporting coal is constant. All owners will live for both periods and there are no government regulations governing the sale of coal. How will Islandia's coal stock be allocated between the two periods? Why? Explain with reference to the incentives facing the individuals in the market. Hint: what type of market does this indicate?