Part II (80 Points) Short Answers. Your answers should be brief but as coogivue wa possible. Pleaps use the back of the page if more writing space is needed 1. (@) Define the following terms: (D) marker failure (b) Explain the Cases themrem and its wipthewhens in a couple of short paragraphs. Your unswer should discuss the relationship of the theorem in externalities the key assumptions under which the theorem holds wwl its relevance for policy purposes [12 points]Assume that the market for gasoline in a country is perfectly competitive. The demand for gasoline is P - 20 - 40 and the industry supply (marginal cost) curve is P = Q + 5, where P is price and Q is quantity. There are no imports or exports. (a) Depict the above demand and supply curves in a clearly labeled diagram and use algebra to calealate the market couilibrium price. P , and quantity, 0*. [ 10 points] (b) Suppose that a policy of putting a ceiling on the price of gasoline at P - 6 is being considered, Depict this price ceiling in your diagram for 2(2). Also calculate the quantity demanded Q" and Quantity supplied O' of gasoline that would result from implementation of the policy- (c) Provide a critical assessment of this price ceiling policy based on your answers to 2(b). Is its implementation likely to increase social welfare? Explain using your diagram for 2(a) and Z (b).3. (a) Provide a mathematical statement and an economic interpretation of Hotelling's Rule for a perfectly competitive non-renewable resource market wist operates over two time periods, ( - 1 and 1 = [10 points] (b) Suppose that X units of a scarce fossil fuel are to be extracted by a perfectly competitive industry over two time periods, t - I and :- 2. Dernand curves for the fuel are given by Pen - how and P2 = a - MD. where 'n' and "b' are positive parameters, while I' and Pa and Q1 and Or denote the respective market prices and quantities sold in periods 1 and 2. For bath time periods, the marginal cost of extracting the fuel is constant at a positive value 'c' and the rate of discount has a positive value 'r'. What does Hotelling's Rule imply about the expected behavior of market equilibrium prices I' and Fx in this model? What can you say about the expected behavior of corresponding market equilibrium quantities Q, and Q2? Also provide explanations for your answers. [10 points] (c) In the context of the two-period model in 3(b), use a set of diagrams to depict the likely effects of a decrease in the total amount available X on the market equilibrium quantity and price in each time period. Also provide economic reasoning for expecting these results. [10 points]