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eco204_HW_8

# eco204_HW_8 - University of Toronto Department of Economics...

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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 8 Question 1 In lecture 8 we saw that if a company uses an imperfect substitutes inputs technology with capital fixed and labor variable: • The short run production function is: q = f(L, k) = Lα kβ • The short run cost minimizing amount of labor is: L = f‐1(q, k) = [q/kβ] 1/α • The short run cost function is: C(q) = PK k + PL L = PK k + (PL /kβ/α)q1/α Suppose the company has constant returns (not the same as constant returns to scale) a) What is the short run production function? b) What is the elasticity of output with respect to labor? Does your answer make sense give the company has constant returns? c) Suppose the company doubles labor. Without using the equation for C(q) what is the impact on total variable cost? Average variable cost? Average cost d) Suppose the company doubles labor. Using the equation for C(q) what is the impact on total variable cost? Average variable cost? Average cost 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain Suppose the company has decreasing returns (not the same as decreasing returns to scale) e) What is the short run production function? f) What is the elasticity of output with respect to labor? Does your answer make sense give the company has constant returns? g) Suppose the company doubles labor. Without using the equation for C(q) what is the impact on total variable cost? Average variable cost? Average cost h) Suppose the company doubles labor. Using the equation for C(q) what is the impact on total variable cost? Average variable cost? Average cost Question 2 Ajax Inc. produces cranberry juice and has the short run cost function C(q) = 5 + Qc. Don Damiano Inc. produces grape juice and has the short run cost function C(q) = 5 + Qg. If Ajax and Don Daminao merge the short run cost function for both cranberry and grape juice is: C(q) = 5 + Qc + Qg. Are there economies of scope if Ajax and Don Damiano merge? 2 ...
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