# answers-midterm2 - Economics 302 Intermediate...

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Economics 302 Silve Parviainen Intermediate Microeconomics Spring 2007 Answers to Midterm II 1P r o f t M a x i m i z a t i o n (a) max π =max l Pf ( l, ¯ k ) wl r ¯ k focs : P ∂f ( ¯ k ) ∂l w =0 = P MP l = w. Since MP l = l - 1 2 l SR = P 2 w 2 and q = ± P 2 w 2 ² 1 2 4 1 2 =2 P w . For w =1and P =2, l =4and q =4. (b) See Graph(1). (c) 1. For w P =3, l =9and q = 6. The pro±ts will be positive, π =3(6) 9 4=5. 2. For w =2and P l q = 2. The pro±ts will be negative, π =2(2) 1 4= 1. 3. For w =1, P =3and r l q = 4 just as in the original short-run equilibrium. The pro±ts will be still negative, π =2(4) 4 2(4) = 4. 2 Cost Minimization (a) Marginal product: the rate at which the ±rm’s total output changes as the quantity of one input is changed keeping all other inputs at constant level. MP l = 1 2 ( l 1) - 1 2 is diminishing because MP l = 1 4 ( l 1) - 3 2 < 0a n d MP l =1 isconstant . (b) For l, k > 0wemusthave MRTS = w r ,or 1 2( l 1) 1 2 = 1 10 = ( l 1) 1 2 =5 = l =26 .

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Since q = l 1+ k = k = q l 1=4
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