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Problem Set #4 1) Suppose fast food firms have production functions of the form: Q = G(FM, Teens) Where: Q is the quantity of fast food produced per week, FM is the number of frying machines leased per week. Teens is the number of teenagers, ages 16-19, employed per week. Let V be the cost of leasing a frying machine for a week and W be the wage required to hire a teenager for a week. Assume the production function, G( ) allows for normal substitution between frying machines and teenagers and produces standard "curved" isoquants rather than the "right angle" isoquants of the one-person-one-computer example we briefly discussed in class. a, Draw a set of diagrams that shows how we begin with isoquants and isocost lines and cost minimization and show how this leads to the total cost curve for a fast food firm. Then show how the total cost curve leads to the average and marginal cost curves. Draw the isocost lines to show equal increments of cost - $10,000, $20,000, $30,000 etc. Then label the isoquant lines so that the resulting total cost curve first shows increasing returns as output expands and then decreasing returns. b. Suppose a technical innovation in frying machines reduces V, the lease cost, by one-half. Use a series of drawings to show (roughly) how this fall in V changes your isoquant/isocost map, the total cost curve, average cost curve and the marginal cost curve. c. The lower lease rate of frying machines means that fewer teenagers will be hired per unit of fast food. Does it follow that fewer teenagers will be hired in the fast food industry? How does the price elasticity of demand for fast food affect your answer? 2) Assume that chickens are produced by many farmers in a perfectly competitive industry. All farmers have identical technologies and minimum average cost is reached at $3.00 per chicken. - On Friday, October 7, 2010, the industry is in long run equilibrium. - On Monday, October 10, 2010, the government imposes a tax of 25 cents per chicken. a) Using appropriate diagrams, draw the equilibrium for the industry and the representative chicken farmer as of October 5. b) Again, using appropriate diagrams, show in both the short run and the long run how the industry and the representative farm adjusts to the 25 cent per chicken tax.b) (10 points) A good's income elasticity is defined as: en = (delta Q/Q.)/(delta I/Io) A luxury good is usually defined as a good with income elasticity greater than +1.0. In other words, holding prices constant, a 1 percent increase in income causes a greater- than-one percent increase in your demand for the good. A second team of economists completes a somewhat different study on your consumption behavior. After observing you reactions to price and income changes, they inform you doughnuts must be a luxury good for you. Is this conclusion consistent with the specific utility function proposed by the first team of economists? Explain your answer.SET A 1. Suppose there is a market for mugs, consisting of 8 people from A to H. The value of one mug to each person is listed in the table below. In addition, each person only wants at most one mug, which means each values the second mug at a price of $0. The suppliers in the market are persons A to D, and each has one mug to sell. Please graph the the market supply and demand curves and show the market price of mugs. (In this case the supply and demand curves should both be discrete). (2 points) Person A C D E F G H Value of mug 4 11 2 13 9 4 2. Now suppose people value the things they own more than the things they don't own (which is a common psychological effect). Consider the previous table as their value of a mug when they don't own it. Suppose that people always value their mug more by $1 than when they don't own it. Graph the new supply and demand curves in the market, and find the new market price for mugs. (The curves should still be discrete). (3 points) Northwestern Economics Tournament Sample Power Round 3. Now forget about the psychological effect in part (2). Suppose people's value of a mug has a uniform distribution on [0, 20], which means any number between 0 and 20 has the same possibility of occurrence (so the average of people's value of a mug is $10). Still we are assuming people only want at most 1 mug. Now we randomly select 100 people, and give 50 of them each a mug, and the rest each 10 dollars. We then let these 100 people engage in mug trade. Derive the expected amount of mugs traded in the market and explain why. (5 points) 4. Finally, let's again consider the psychological effect in part (2), but instead of $1, people now value the mugs they own by $2 more. In the same scenario under part (3), find the new expected amount of mugs traded in the market of 100 randomly selected people and explain why. (Note: The distribution of people's value of a mug in part (3) is for if they don't own a mug.) (3 points)SET B 1. Draw a graph representing an unregulated monopolistic firm. In your graph, label. a. The demand, marginal revenue, marginal cost, and average total cost curves. (4 points) b. The profit-maximizing quantity and price. (2 points) c. The areas of economic profit and deadweight loss. (2 points) 2. Suppose now that the monopolistic firm can practice perfect price discrimination. Redraw the graph above and label. a. The demand, marginal revenue, marginal cost, and average total cost curves. (4 points) h. The profit-maximizing quantity. (1 point) c. The area of economic profit. (1 point)SET C Suppose two people A and B are on two different islands. A's island is surrounded by rigid cliffs but has a lot of coconut palms, while B's island is covered by desert but has shallow water teeming with fish. A and B can both work for 6 hours per day. It takes A 90 minutes to catch a fish and 20 minutes to gather a coconut, while it takes B 30 minutes to catch a fish and 60 minutes to gather a coconut. 1. Draw the production possibility frontiers (PPFs) of the two men on the same diagram, with daily production of fish on the vertical axis and of coconuts on the horizontal axis. What is A's opportunity cost of a coconut in terms of fish? What is B's opportunity cost of a fish in terms of coconuts? (4 points) 2. Initially A and B don't know of each other's existence, so there is no trade. According to their own taste of fish and coconuts, unfortunately, A decides to spend all his time gathering fish and B decides to spend all his time gathering coconuts. How many fish will A consume each day? How many coconuts will B consume each day? (2 points) 3. One day they spot each other on their own islands, and they decide that it's a good idea to engage in trade. Now they specialize in producing what they are more efficient at and trade fish for coconuts one-for-one. Is it possible for them to be both better off after this trade? If so, describe a trade that makes them both better off. If not, explain why. (2 points) 4. Evaluate the following statement: if A is more efficient than B in both gathering coconuts and catching fish, A should not trade with B. (3 points)