eco204_HW_7

eco204_HW_7 - University of Toronto, Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain ECO 204 2008‐2009 Ajaz Hussain HW 7 PART A In lectures 7 and 8 we discussed why demand for labor and capital were: • • • In the case of imperfect substitutes technology q = Lα Kβ functions of PL and PK In the case of perfect substitutes technology q = αL + βK independent of PL and PK In the case of complements technology q = min(αL, βK) independent of PL and PK In Part A you will practice these statements. Question 1 Ajax uses an imperfect Substitutes technology with long run production function q = Lα Kβ . Currently, α = ½ β = ½, PL = \$1 and PK = \$2. a) Interpret Pk. b) Suppose demand for Ajax’s product is given the equation P = 100 ‐ 10q. What is Ajax’s target output if it wants to maximize revenues? c) Given the target output q in part (b), how many workers should Ajax hire? How much capital should Ajax lease? d) What is the long run cost of producing the Ajax’s target output? 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain e) Suppose Ajax’s workers clamor for higher wages. The labor union negotiates a higher wage of PL = \$2. With the expenditure in part (d), will Ajax be able to produce the target output? f) How will Ajax react to higher wages? In particular, what is the percentage change in labor, capital and long run cost due to the higher wages? Question 2 Jenn uses a complements technology with long run production function q = min(αL, βK) . Currently, α =1/2, β =1/2, PL = \$10 and PK = \$10. a) Suppose demand for Jenn’s product is given the equation P = 100 ‐ 10q. What is Jenn’s target output if she wants to maximize profits? b) Given the target output q in part (a), how many workers should Jenn hire? How much capital should Jenn lease? c) What is the long run cost of producing Jenn’s target output? d) Suppose Jenn’s workers clamor for higher wages. The labor union negotiates a higher wage of PL = \$20. With the expenditure in part (d), will Jenn be able to produce the target output? e) How will Jenn react to higher wages? In particular, what is the percentage change in labor, capital and long run cost due to the higher wages? Question 3 In‐Hart uses a perfect substitutes technology with long run production function q = αL + βK. Currently, α =1, β =1, PL = \$10 and PK = \$20. a) Suppose demand for In‐Hart’s product is given the equation P = 100 ‐ 10q. What is In‐ Hart’s target output if he wants to maximize profits? b) Given the target output q in part (a), how many workers should In‐Hart hire? How much capital should In‐Hart lease? c) What is the long run cost of producing In‐Hart’s target output? d) Suppose the price of leasing capital is volatile. For what range of PK will In‐Hart use the same number of workers and capital as in part (b)? 2 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain PART B In this part you will practice the difference between long and short run production functions, demand for labor and capital, and cost function. Question 4 Ajax Corporation has production function q = Lα K1/2 and has target output q. Currently, PL = \$1 and PK = \$1. Long Run: a) Under what conditions will Ajax have constant returns to scale? Interpret constant returns to scale. b) For a given value of α, what is Ajax’s long run demand for labor and capital? c) For a given value of α, what is Ajax’s long run cost function? d) Will Ajax’s long run AC decline, remain constant, or increase with q? Short run: Suppose K = 100. e) Under what conditions will Ajax have constant returns? Interpret constant returns. f) For a given value of α, what is Ajax’s short run demand for labor? g) For a given value of α, what is Ajax’s short run cost function? h) Will Ajax’s short run AC decline, remain constant, or increase with q? 3 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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