Questions please answer

Problem Set 1 1. (25 points) For each of the following scenarios, use a supply and demand diagram to illustrate the effect of the given shock on the equilibrium price and quantity in the specified competitive market. Explain whether there is a shift in the demand curve, the supply curve, or neither. (a) (5 points) An unexpected temporary heat wave hits the East Coast. Show the effect in the ice cream market in New England. (b) (5 points) The government introduces a tax on ice cream which is paid by producers. What is the effect in the ice cream market? (c) (5 points) China and Mexico are major producers of textiles. Workers in Mexico decide to go on strike. Show the effect on the market for Mexican textiles. (d) (5 points) Show the effect of the situation described in (c) on the market for Chinese textiles. (e) (5 points) Suppose the government imposes a price cap on bottled water. Show the effect in the bottled water market. Problem 1 courtesy of William Wheaton. Used with permission. 2. (20 points) For each of the following pairs of goods, identify which one you would expect to have more own-price elastic demand. Please explain your reasoning. (a) (5 points) Computers (generally) vs. Apple MacBook Pro laptops. (b) (5 points) Stereo headphones (generally) vs. hearing aids. For each of the following goods, identify whether you would expect demand to be more (own-price) elastic in the short run or the long run. As above, please briefly explain your reasoning. (c) (5 points) Retail gasoline in the suburbs of Chicago. (d) (5 points) Air conditioning units in Miami Beach, Florida. Problem 2 courtesy of Luke Stein. Used with permission. 3. (30 points) Consider the market for apple juice. In this market, the supply curve is given by Qs = 10Py -5PA and the demand curve is given by QD = 100 -15Py + 10Pr, where J denotes apple juice, A denotes apples, and T denotes tea. (a) (7 points) Assume that PA is fixed at $1 and Pr = 5. Calculate the equilibrium price and quantity in the apple juice market. (b) (7 points) Suppose that a poor harvest season raises the price of apples to PA = 2. Find the new equilibrium price and quantity of apple juice. Draw a graph to illustrate your answer. (c) (8 points) Suppose PA = 1 but the price of tea drops to Py = 3. Find the new equilibrium price and quantity of apple juice. (d) (8 points) Suppose PA = 1, Pr =5, and there is a price ceiling on apple juice of P; = 5. What is the excess demand for apple juice as a result? Draw a graph to illustrate your answer. Problem 3 courtesy of William Wheaton. Used with permission. 4. (25 points) You have been asked to analyze the market for steel. From public sources, you are able to find that last year's price for steel was $20 per ton. At this price, 100 million tons were sold on the world market. From trade association data you are able to obtain estimates for the own price elasticities of demand and supply on the world markets as -0.25 for demand and 0.5 for supply. Assume that steel has linear demand and supply curves throughout. (a) (10 points) Solve for the equations of demand and supply in this market and sketch the demand and supply curves. (b) (15 points) Suppose that you discover that the current price of steel is $15 per ton and the current level of worldwide sales of steel is 150 million tons. The most recent elasticity estimates from the trade association this year are -0.125 for demand and 0.25 for supply. Describe the change in the supply and demand curves over the past year using your diagram from part (a). What sort of event (s) might explain the change?Question 1 (20 points) Consider the balance sheet of an American bank before the crisis. On the liabilities side, the bank has a total capital of 10 billion dollars and deposits worth of 150 billion dollars. On the assets side, 10% of the assets are subprime mortgages. The rest of assets are considered safe and will not go through changes in value. 1. What is the leverage of this bank? (6 points) 2. Suppose that after the outbreak of the crisis, the value of the subprime loans falls by a half. Is the bank still solvent? What is its new leverage? (6 points) 3. According to the Basel III rule (the international rule that determines banks' minimum required capital, try to google it out if you haven't heard about it before), banks are supposed to have a leverage ratio of at most 2. Does this bank need to recapitalize? If so, by how much? (8 points) Question 2 (30 points) Assume a bank has a certain amount of debt, D, that is 5 times as much as its own capital. Assume that a third of the bank's money is invested in some risky investment with a random rate of return @ (0 dollars back for 1 dollar invested). Assume that o follows a uniform distribution with a support ranging between 0 and 2. 1. Draw the bank's balance sheets today and tomorrow, assuming it will be solvent. (10 points) 2. Determine the critical value of o below which the bank is not solvent. What is the probability that this happens? (10 points) 3. Assume that the bank wants to stay solvent in 90% of cases. What can it do? (Hint: you should think about both reducing its exposure to risks or increase its capital.) (10 points) Question 3 (50 points) Consider the standard version of the Holmstrom Tirole model we discussed in class. 1. Consider first the case of direct investment (i.e. with no banks). Prove that there is a minimum amount of net worth, A, that entrepreneurs need to have to start the projects. (10 points) 2. Now suppose that no entrepreneurs in this economy have sufficient net worth so no projects are started in equilibrium. If you are a social planner, is there a way to redistribute initial wealth (only before the projects get started) in this economy to make a Pareto improvement (a Pareto improvement is a situation in which all agents in this economy are better-off)? What happens if instead of focusing on Pareto improvements, you only care about the GDP (or total investment)? (12 points) 3. Now let's put banks back into the story. Recall that we denote by 8 the rate of return that a bank can obtain if it invests elsewhere. Show that there is a minimum amount of capital, Ip, that banks have to contribute to the projects for there to be active monitoring. (10 points) 4. Assume that b + c B? (13 points) 5. What happens for entrepreneurs if A /? (5 points)Bank Run Model (40 points) This exercise leads you to go through the derivation of the bank run model. There are 3 periods. At t = 0, all agents start with 1 unit of endowment and can invest in 2 different technologies: 1. A short term technology that delivers 1 unit of output at t = 1 for each unit of output invested at t = 0. 2. A long term technology that delivers R > 1 units of output at t = 2 for each unit of output invested at & = 0. However, if this technology is liquidated at t = 1 it delivers L