Question

2. Assume a firm can produce according to the production function: ? = ?(?, ?) = ? + 3?

1. Assume the wage, the cost of labor, is 6, and rent the cost of capital, is 12. What is the best combination of labor and capital to produce 12 units with?

2. Illustrate your answer to part a with an isoquant/isocost drawing.

3. If the wage decreased to $2, would this change how the firm will produce? If so, how?

3. Assume a firm can produce according to the production function: ? = ?(?, ?) = min {2?, ?}.

1. Assume w is 2 and r is 3. Find the cost minimizing combination of labor and capital that produces 10 units.

2. Illustrate your answer to part a with an isoquant/isocost drawing.

3. Find the cost function ?(?, ?, ?).

Answer 1

→ -> _ML MP MA MP- 1 Non 74 3 2 e-Isoquant 4 12 9 - L+3k ,w=6 , R 12,9 -12 At equilibrian, slope of isoquant should be equal to slope of isocost -MRTS LAW 9-L+3K - MP = 2a = 1 and MPR = 8 9 = 3 * IMRTS = 1 and slope of isoquant = t-W1=1 6 1 = 1 ie. For this scenario, slope of isoquant (!) < slope of esocost (1) darges The firem will use mare capital, and use only capital as long as the slope of is o quant a slope of isocost. q=L+3K - 12 ->O+3K - 12 -> 3K-12 -> K24 fiy) =) Firem will use no labor and 4 units of capital to preuduce 12 units of output As shown in fig. 1, the iso quant is shown by AB, and there are 3 iso ost.()., (241C). At pånt A, isoquant meets 16, which is the optimal solution. L 97 wages decreases to $2... >2. Now slope of 130 cost = 7 / 2 = t. slampe of esoquant le 3) > slepeof isocoste +) Fig. 2) - Firem will use only labor. L+3K=12 > L+360) =12 ->L=12] -> Firm will use no capital and in laberto produce q=12. In fig 2, the optimal bundle is shown at B where isoquant AB meets is ocost 162 3 q = minal, k} ,ws 2 and 3 In this case, firem must opereate where aL=k=q Sothon 2L= q = L = 96 and k=9 ) Firem must use L= q of labor and kaq of capital to produce k. >> Costica) 2[?] +3[9] - 4+39 - 49 ->c(a)=49] cost function 9f9-40, L=42=5 and k=9-10 Firm uxs s units of labor and 10 units of capital Figu Shaus Kü L-shaped roquaint and to cost and me optimal pont (€) with Suits of labor and to unit of capital 414 A Isoquant 3 2 L ! =WL+ck = 2 ཙི་ནའི་ Procesi L 2