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EXERCISE Question 1 (Three-period Model - Appendix to Ch. 4) A consumer lives three periods - the learning period, the working period, and the retirement period. Her income is 100 during the learning period, 1000 during the working period, and 400 during the retirement period. The real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime. 1) Assuming no borrowing constraint, what are the consumption and saving in each period? Period Desired Consumption Desired Saving Learning Period Working Period Retirement Period 2) Assuming that the consumer faces a borrowing constraint that prevents her from borrowing, what is the consumption in each period? Period Desired Consumption with Borrowing Constraint Learning Period Working Period Retirement Period Question 2 (Two-period Model on Budget Line and Indifference Curve - Appendix to Ch. 4) Part I - Constructing Budget Line and the Changes in Interest Rate and Asset Suppose Alice earns $10,000 today and expects to earn $18,000 tomorrow. The real interest rate is 20%. 1) With current and future consumption on horizontal and vertical axes, respectively, draw Alice's budget line. Precisely calculate the intercepts and denote the no-borrowing-no-lending point. Write down the budget constraint equation. 2) Suppose the real interest rate is 100%, repeat 1). 3) Suppose, instead of the increase in real interest rate, Alice finds $10,000 in her attic today. Draw her new budget line. Part II - Finding Optimal Consumption Plan 4) From Part I, assuming no borrowing constraint. Suppose Alice desires perfectly smooth consumption over her lifetime, give the method on how to find her optimal consumption plans. 5) "When interest rate decreases, a borrower will not become a saver, but a saver may become a borrower." Use the budget lines and indifference curves to show the optimal consumption plans that correspond to the statement. Part III - Substitution Effect and Income Effect 6) Draw the budget lines and indifference curves that corresponds to both cases of borrowing and lending consumer facing a decrease in interest rate. Decompose the substitution and income effects.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.would cause the number of smokers to fall by 2-3 percent. By most people's definitions of significant, that is not very large. c) (10 points) Suppose that after analyzing the problem, you were told that during the 1980s, the total number of persons over 15 years old had been growing at 5% per year. Does this fact change your answers to (a) and (b)? Explain why or why not.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