Economics 111 Exam 1 Fall 2005 Prof MontgomeryAnswer all questions. 100 points possible. 1. [20 points] Policymakers are concerned that Americans save too little. To encourage more saving, some policymakers have suggested imposing a “consumption tax” on the portion of income that is spent rather than saved. To explore the effects of this type of tax, we might begin with the model discussed in lecture. Suppose a consumer will live two periods, with consumption level x1in period 1 and consumption level x2in period 2. The consumer’s utility function is given by U(x1, x2); assume that both goods are normal goods. The consumer has income I in period 1, and no income in period 2. However, the consumer can save some of her income in period 1 in order to have positive consumption in period 2. Any income saved in period 1 is placed in the bank, earning interest at rate r. Given no consumption tax, period 2 consumption is thus given by x2= (1+r)(I – x1). Now suppose that consumption in period 1 (but not period 2) is subject to a consumption tax. More specifically, suppose that consumption in period 1 is taxed at rate t. Thus, if the consumer chooses x1, she must also pay tx1in taxes. Consequently, period 1 saving becomes I – (1+t)x1, and period 2 consumption is given by x2= (1+r)(I – (1+t)x1). (a) Using a graph, show how the consumption tax affects the consumer’s budget constraint. Then, reasoning about substitution and income effects, discuss how the consumption tax will affect consumption and savings in period 1. [HINT: Savings in period 1 are proportional to consumption in period 2.] (b) If the consumption tax was instead imposed on consumption in bothperiods, how does this change your answers to part (a)? [HINT: The consumer’s bank balance in period 2 must now cover her consumption plus her tax payment in period 2.] 2. [30 points] Consider a firm with variable cost function VC(Q) = 10Q + 2Q2, where Q is the quantity produced by the firm. The firm has fixed costs FC = 98. Assume that all fixed costs are sunk costs. a) Derive the firm’s marginal cost (MC), average cost (AC), and average variable cost (AVC) functions. Then plot the MC, AC, and AVC curves for Q between 0 and 12. [HINT: You can solve this problem by constructing a table or by solving analytically for these functions using calculus. Your graph doesn’t need to be perfectly to scale, but should be properly labeled and indicate relevant x and y coordinates on the axes.] b) Suppose that the firm has already entered the market, and can sell each unit of output at price P = 50. Compute the firm’s optimal quantity and profit level. If the price falls to P = 30, compute the firm’s new optimal quantity and new profit level. c) How low would the price need to fall before the firm exits the market? If the firm had not yet entered the market, what is the lowest price at which entry would occur? Explain how your answers can be determined from your graph in part (a).
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