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solutions4[1]

# solutions4[1] - EC201 Fall 2007 Prof Jordi Jaumandreu...

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EC201, Fall 2007, Prof. Jordi Jaumandreu Solutions to Problem set #4 Costs 1. Call H the number of hours, then the expression for cost is C = wH = 8 H. The implicit production function is q = 4 H , where q is the number of o ces. This implies H = q 4 , expression that substituted for H in the expression of cost gives the cost function C = 2 q. This (linear) cost function implies the same constant average and marginal cost: MC = AC = 2 . If a franchise lump-sum tax of 30 is imposed we have a new cost function C = 30 + 2 q, which gives an average cost AC = C q = 30 q + q while MC = C q = 2 2. This is a case of increasing returns to scale by purely technological reasons. A crate of 1 cubic-foot needs 6 sides of a square-foot and this implies a total cost of \$6. A 8 cubic-foot needs 6 sides of 2 square-foot, each side of 2 square-foot needs 4 square-foot and this implies a total cost of \$24. In general, calling V to the volume, we have C = 6( 3 V ) 2 = 6 V 2 3 . AC (1) = C ( 1 ) 1 = 6 , AC (8) = C (8) 8 = 24 8 = 3 and, in general, AC ( V ) = C ( V ) V = 6 V 1 3 .

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