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and w = 1 (for labor). On an optimal choice diagram with K on the horizontal axis and L on the
vertical axis, show the optimal choices of K and L when Q = 5. Draw the isoquant for Q = 5,
indicate the optimal basket or baskets of inputs, and calculate the total cost. ! L$
b) Consider further the production function Q = min " K , % . Assuming w = 1 and r = 8, what
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is the long run total cost function C(Q) for this firm? [Hint: This one is easier than it looks!] Labor,!L Answer:
3) a) The isoquant Q = 5 is shown for this Leontief technology. To produce Q = 5, the firm will
need at least K = 5 and L = 20. This will cost the firm C = wL + rK = 1(20) + 8(5) = 60. The isocost
line representing an expenditure of 60 is drawn. The optimal basket of inputs is A.
How$to$produce$5$units$of$
output$using$capital$($8$per$
unit)$and$labor$($1$per$unit) !100 !8 0 60 40 A !20 Q$=$5$IsoQuant
TC$=$$60$IsoCost$
has$slope$of$–r/w$=$E8/1 !!!0
!!!0 !5 10 15 !2 0 !25 Capital,!K b) This is a Leontief function, so the firm will always use L = 4Q and K = Q, which is found at the
elbow of the Lshaped...
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This homework help was uploaded on 03/03/2014 for the course ECON 310 taught by Professor Whinston during the Spring '12 term at Northwestern.
 Spring '12
 Whinston

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