3. A firm employs labor and capital by paying $40 per unit of labor (MCL) and $200 per hour to rent a unit of capital (MCK). The production function is given by Q=30L-2L2+ 120K -3K², where Q is total output. a. Derive MPL and MPK b. Determine the firm's optimal combination of capital (K) and labor (L)? Hint state the combination in the format L = C. Using your answer in part b, if the firm is committed to spending $3,240 on capital and labor per hour, how many units of labor (L) and capital (K) should the firm employ. Recall that the firm is paying per unit of labor and $200 per hour to rent a unit of capital. $40 d. How much output (Q) is produced if the firm uses the input values found in the previous question?

Company Z has the following data corresponding to the production function. Where (L) is the amount of the labor factor and (K) capital. Q=K0.4 L 0.6 a) Calculate the amount of production, applying the production function for each of the respective values of K and L. K L Q 10 80 30 160 50 320 70 640 90 1200 a) Graph the amount of production obtained on the Y axis, and with the labor input on the Х аxis b) Draw isoquant lines for each level of production, placing capital on the Y axis and labor on the X axis, to better appreciate the displacement.

QUESTION 39 The folllowing table shows data for a simple production function. Capital (K). Labor (L) 10 0 10 1 10 2 3 4 5 6 10 10 10 10 TP or Q AP MP 6 14 20 14 8 Assume that the cost of capital, PK, is $50 per unit, and the cost of labor, PL, is $100 per unit. Marginal cost, MC, is at minimum when labor, L, is equal to O2 units. O4 units. O 3 units. 5 units.

Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s costminimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.d) Determine this firm’s minimum cost of producing 120 units.e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s costfunction C(Q). Show your work.

***QUESTION HAS FOUR PARTS - ALL PARTS MUST BE ANSWERED TOGETHER AS THEY ARE DEPENDENT ON EACH OTHER***   1. A farmer raises apples using land (K) and labor (L), and has an output of ? (?,?) = ? 0.5 ? 0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis.   b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve?   c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?   d. In the long run, the farmer can change both his amount of land and his amount of labor. Suppose…

Cobb Douglas production function..? Solve this I'll Upvote your work

Grease Tech produces oil changes. The production of oil changes reles on both capital (K) and labor (L) and is combined in the following production function F (K, L) = KILL Take the derivative of this production function with respect to capital. What is the marginal product of capital evaluated at (le. just plug in the numbers) 64 units of capital used and 16 units of labor?

Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.

Please Solve the answer can u see in option im needed max in 15-20 minutes thank u

Could you please help me with this question? Thank you!