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University of Alberta - Department of Economics - Winter 2010 ECON 281 - Intermediate Microeconomic Theory I - B3 - Marchand ASSIGNMENT 2 - (100...

1.) The Alberta Metal Co. produces brass fittings. AMC’s engineers estimate the production function as , where q is annual output in pounds, L is labor in person hours, and K is capital in machine hours. The marginal products of labor and capital are and respectively. AMC’s employees earn $15 an hour and the firm estimates a rental charge of $50 on capital. In addition, AMC forecasts annual costs of $500,000 per year. (40 pts) 8.06.0500KLq⋅⋅=.04.0300KLMPL⋅⋅=−82.06.0400−⋅⋅=KLMPK
a.) Determine how much capital and labor the firm should employ given their budget. How much output can they produce? (15)
AMC is currently negotiating with a newly organized union. The firm’s personnel manager indicates that the wage may rise to $22.50 under the proposed contract.
b.) Analyze the effect of the higher union wage on the firm’s use of inputs. By what percentage does the firm’s output change? (15)
c.) Draw out the equilibrium in parts (a) and (b) in separate graphs (label all). (10)
University of Alberta – Department of Economics – Winter 2010 ECON 281 – Intermediate Microeconomic Theory I – B3 – Marchand ASSIGNMENT 2 – (100 points total) Please demonstrate your understanding of the calculations required in microeconomics by answering the following three questions covering material from Chapters 7 and 8. Your own, original work should be submitted on: Friday, March 19 th , by 4:00pm . Assignments not handed in during class time should be handed in to the economics department drop box. Show all of your steps and say what you are doing for each step. 1.) The Alberta Metal Co. produces brass fittings. AMC’s engineers estimate the production function as , where q is annual output in pounds, L is labor in person hours, and K is capital in machine hours. The marginal products of labor and capital are and respectively. AMC’s employees earn $15 an hour and the firm estimates a rental charge of $50 on capital. In addition, AMC forecasts annual costs of $500,000 per year. (40 pts) 8 . 0 6 . 0 500 K L q = . 0 4 . 0 300 K L MP L = 8 2 . 0 6 . 0 400 = K L MP K a.) Determine how much capital and labor the firm should employ given their budget. How much output can they produce? (15) AMC is currently negotiating with a newly organized union. The firm’s personnel manager indicates that the wage may rise to $22.50 under the proposed contract. b.) Analyze the effect of the higher union wage on the firm’s use of inputs. By what percentage does the firm’s output change? (15) c.) Draw out the equilibrium in parts (a) and (b) in separate graphs (label all). (10) 2.) Leduc Dairy Farm’s cost function is () 5 / 1 5 / 6 72 A q q C = , where q is the amount of milk output and A is the average age of employees. This year, the average age is 32, but with some new hires expected next year, the average age will lower to 29. (20 pts) a.) Calculate the change in costs between this year and next. (10) b.) What is this firm’s relationship between average age and cost and why might a firm have this particular relationship? Explain. (10) 3.) Consider a competitive market in which the market demand and market supply for a product are given by q p = 5 . 1 75 and q p + = 5 . 0 25 q MC respectively. The typical firm in this market has a marginal cost of + = 10 5 . 2 . (40 pts) a.) Determine the equilibrium market price, market quantity, and the quantity provided by a typical firm. (15) Suppose market demand increased to q p = 5 . 1 100 . b.) Recalculate all of the values from part (a). What are the percentage changes in the market and firm quantities? (15) c.) If part (a) represented a long-run equilibrium, would part (b) represent a new long-run equilibrium for the typical firm? Explain. (10)
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This question was asked on Mar 16, 2010.

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