econ 111 - exams - 2006

econ 111 - exams - 2006 - Economics 111 Exam 1 Fall 2006...

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Economics 111 Exam 1 Fall 2006 Prof Montgomery Answer all questions. 100 points possible. 1) [23 points] Consider a market with demand function Q D = 100 – 2P and supply function Q S = – 40 + 5P where P represents price. a) Compute the equilibrium price and quantity. If the current price was 15, would there be a shortage or a surplus? How large would this shortage/surplus be? b) Suppose that supply changes so that Q S = –26 + 5P (while the demand function remains the same as above). Compute the new equilibrium price and quantity. c) Given the change in price and quantity from the old equilibrium (part a) to the new equilibrium (part b), compute the elasticity of demand. Is the demand curve (in the region under consideration) elastic or inelastic? Compute sellers’ revenue for parts (a) and (b). In the present example, did the change in price cause revenue to increase or decrease? More generally, how does the elasticity of demand affect the relationship between change in price and change in suppliers’ revenue? 2) [32 points] A firm’s long-run production function is given by Q = K 1/3 L 1/2 where Q = quantity of output, K = capital, and L = labor. However, in the short run, suppose that capital is fixed at K = 64 while labor remains a variable input. Thus, the firm’s short-run production function becomes Q = (64) 1/3 L 1/2 = 4 L 1/2 = 4 L . Further assume the wage per unit of labor is w = 2 and the price per unit of capital is r = 3. a) Focusing on the short-run case, derive the firm’s variable cost, total cost, marginal cost, and average cost functions. [HINT: You may answer by constructing a table with a column for each function, or else compute these functions analytically. If you construct a table, you might try increasing quantity by increments of 8.] b) If the product price is P = 12, what is the optimal quantity (Q*) chosen by the firm? Compute the firm’s profit (or loss) given production at this optimal quantity. Plot the firm’s MC and AC curves. Using this graph, how is the optimal quantity determined? What area corresponds to the firm’s profit or loss? c) Still focusing on the short-run (with K fixed at 64), suppose the price of capital rises to r = 5. (As above, assume w = 2 and P = 12.) How does this affect the firm’s MC and AC functions? Compute the firm’s optimal quantity (Q*) and profit/loss. d) Conceptually (without doing any numerical computation), how would the firm adapt to the increase in the price of capital in the longer run? Illustrate your answer using an isoquant diagram.
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3) [30 points] Consider a worker who has 1000 total hours per year that may be allocated between work and leisure. Thus, letting H = work hours and L = leisure hours, the worker has a time budget H + L = 1000. The worker earns w = $30 per hour and has no non-labor income. a) Suppose the government taxes income at a 20% rate.
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econ 111 - exams - 2006 - Economics 111 Exam 1 Fall 2006...

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