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Question 1 Let an individual's utility function be given as w(x1, *2) = 2 \\x1 X2. a) Compute the Marginal Rate of Substitution. b) Initially, the individual consumes bundle (x] = 100, x2 = 12.5). Then, the indi- vidual's consumption of the first good is cut to x, = 50. What is the new level of consumption of good 2, x2, that the individual needs to consume in order to reach the same utility level as before? c) Given the prices p1 = 1 and p2 = 2 for the first and the second good, respec- tively, and a budget of m = 100, what is the best consumer choice? d) Find the individual's general demand function for good 2. e) If the price for the first good rises to p; = 50, how much less of good 2 will the individual conusme? f) Assuming the demand function for good 1 is x, (p, ) = : ", what is the inverse demand funtion, and what is the own-price elasticity of demand for good 1! g) Assuming the demand function for good 1 is x(p1) = , ", show mathematic cally that the good is not inferior.1) (25 points). At different times, federal, state and local governments have intervened in markets by imposing various price controls. In 1971, President Richard Nixon imposed a partial set of price controls to help reduce the nation's inflation. The controls applied to many goods sold retail to consumers but they did not apply to many goods sold from one business to another. In particular, the law set a maximum price per pound at which chickens could be sold in food stores. But the law did not apply to feed corn that farmers used to raise the chickens. Feed corn prices continued to rise. a) (10 points) How would you expect the retail market for chickens to develop over time if the maximum retail price of chickens was fixed by law but the price of feed corn used for chickens continued to rise? Illustrate your answer using appropriate diagrams.b) (5 points) In a standard supply-demand equilibrium, anyone who is willing to pay the market price can purchase the good. Was that condition likely to hold in the 1971 retail market for chickens? Explain why or why not. If the condition did not hold, describe what other factors beyond price might determine which consumers purchased chickens.c) (10 points) It takes about 60 days to raise a chicken from the time the egg is laid to the time the meat is sold in a supermarket. Under normal conditions, ranchers like to feed a cow for four years before turning it into beef. Assume that 1971 price controls applied to the price of retail beef but not to cattle feed and these retail price controls were expected to continue. How, if at all, would the behavior of the retail market for beef have differed from the consumer market for chickens? Illustrate your answer with appropriate diagrams.2) (30 points) In 1982, cigarette consumption in the United States totaled about 30 billion packs at an average price including tax of $.85 per pack. In 1983, Congress passed a general tax bill including a temporary increase of the federal tax on cigarettes from $.08 to $.16 per pack. In 1984, cigarette consumption dropped to 29.5 billion packs. a) (10 points) Given this information, what was the approximate price elasticity of demand for cigarettes? In your answer, assume the only change in price between 1982 2 and 1984 involved the change in taxes. Would you describe this portion of the demand curve as elastic or inelastic?b) (10 points) In 1985, the $.08 per pack tax was due to expire. Some experts argued that rather than cutting the federal tax in half, the federal tax ought to be doubled to $.32 per pack on the grounds that it would significantly reduce the likelihood that a person would smoke cigarettes. Explain why you agree or disagree that doubling the tax would have this effect.3) {3H points] You live in Seattle a hundred years from now when human beings have evolved {at least in Seattle) to the point where they consume only two goods: cups of coffee and doughnuts. Coffee costs 31(1) a cup and doughnuts cost $23!] a piece. a] {ID points] Economists can never directly observe utility Jnctionsthey ntust estimate utility functions based on observed behavior. After careful study of your buying patterns, a learn of economists tell you that your utility function looks like this: U [CD] = liLNtC] + 4LNED} Where: C is the number ofcups of coffee you drink D is the number of doughnuts you eat And your income is $64.00 If the economists are right, calculate your utility maximizing combination of cups of coffee and doughnuts. 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