3. (parts a to e) Suppose that total oil reserves are known to be 100 units. For planning purposes, the world can be divided into three periods (t = 0, 1 and 2). The inverse demand curve for oil in the three periods is given by: Pt= 100 qt The marginal extraction cost is $10 and the discount (interest) rate is 10%.

a. Write down the socially optimal (dynamically efficient) allocation problem.

b. Calculate the dynamically efficient quantities extracted and the prices in each period.

c. Find the shadow price of the oil reserves and the MUCs.

d. Is Hotellings rule satisfied? Explain by including a definition of this rule.

e. If new exploration prove that the current reserves is more than it was believed and it is 350 units how your solutions to parts b and c change? (10points)