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6. A manufacturer uses labor and capital to produce widgets. Labor and capital are perfect substitutes and the production fun
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(a) The completed table:

Isoquants Isocost Lines TC=10 | TC=15 Q=20 Q=40 L K=10-0.5L L K=20-0.5L 10.0 7.5 0 10 2010 10 15 100 151 5.0 own|Ել 2.5 0.0 3

Isoquants for Q=20 and Q=40 IQ=20 IQ=40 Quantity of Capital (K) 0 5 10 30 35 40 15 20 25 Quantity of Labour (L)

(b) Graphs of isocost lines of $10 and $15 when w=$1 and v=$1

Isocost Lines for TC=10 and TC=15 Isocost Line-1 Isocost Line-2 Quantity of Capital (v=$1) 0 1 2 3 12 13 14 15 4 5 6 7 8 9 10

(c) To isoquant to produce output Q=20 touches the Isocost line at point where L=10 and K=5.

Thus L=10 and K=5 combination minimizes the cost.

Hence at this point, TC=2K+1L=2*5+1*10=10+10=20

Isoquants Q=20 and Isocost Lines 15.0 14.0 13.0 12.0 IQ=20 +Isocost Line-1=10 Isocost Line-2=15 10.0 Quantity of Capital (K)

(d)We know that MRTSLK=MPL/MPK=w/v

Here MPL=1 and MPK=2

Thus, w/v=1/2=>v=2w

Thus if v=$1, w=$2

Then the cost can be minimized otherwise cost minimization.

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