Question

#6

6. A manufacturer uses labor and capital to produce widgets. Labor and capital are perfect substitutes and the production function is Q-2K+IL a. Derive and graph the isoquants for Q-20 and 0-40 units of output (not all units of K will be whole numbers) (20 - 2K+ILK -10-0.5L.) 0-20 LK 040 LK 10 b. Suppose the price of labor is w 51 and the price of capital is for a total cost of $10 and $15. 51. Graph the socotines c. How much of each input will the firm use to minimize the cost of producing Q-20 units of output? Explain. d. Is the MRTS w/y at the point of cost minimization? WHY or WHY NOT? 14 12150 21340 TIT

Answer 1

Answer:

(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 30 40

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 11 Quantity of Labour (w=Sl)

(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) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Quantity of Labour (L)

(d)We know that MRTS_LK=MP_L/MP_K=w/v

Here MP_L=1 and MP_K=2

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

Thus if v=$1, w=$2

Then the cost can be minimized otherwise cost minimization.