W14 MIC Problem Set 5 Solutions

# W14 MIC Problem Set 5 Solutions

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Unformatted text preview: pital) # 4& 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 # 4& 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 L-shaped...
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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.

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