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s06-answers-midterm2-4 - Economics 302 section 4...

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Economics 302, section 4 Silve Parviainen Intermediate Microeconomics Spring 2006 Answers to Midterm Examination II 1 Production Technology (a) The percentage by which output will increase when all inputs are increased by a certain percentage. This function exhibits constant returns to scale, since f ( tl, tk ) = ( tl ) 1 2 ( tk ) 1 2 = tf ( l, k ) . (b) Technological progress occurs if q 1 < q 2 or q = l 1 2 k 1 2 < l 1 2 k 3 4 . This is true for all l > 0 , k > 1. (c) The firm will move towards more capital intensive production since MRTS 1 = k l > 2 k 3 l = MRTS 2 . 2 Cost Minimization (a) At the optimum, MP l MP k = 1 2 l 1 2 = w r = l = r 2 w 2 . Substituting l in the production function yields q = r 2 w 2 + k = k = q r 2 w . The optimal cost function is TC = w r 2 w 2 + r q r 2 w = rq r 2 2 w . (b) If q = l + ¯ k , then l SR = ( q ¯ k ) 2 and the short-run optimal cost function STC = w ( q ¯ k ) 2 + r ¯ k.
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3 Competitive Firm (a) The short-run supply function is the part of the MC curve that lays on or above the AVC curve: MC = 2 q + 2 = q + 2 = AVC = q = 0
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