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- The production function of a firm is f : R² → R, (L, K) + 10L + 16K – 2L? – K?, and the per unit costs of the quantities of labor input L and capital input K are 4 and 2 dollars, respectively. The firm wants to maximize its production of output subject to the total cost of production not exceeding 20 dollars. The firm can only employ non-negative quantities of labor and capital. (a) Write the firm's problem as an optimization problem with inequality constraints. (b) Identify any points in the constraint set that violate the non-degenerate constraint. qualification for the problem in (a). (c) Construct the Kuhn-Tucker Lagrangian by defining L(L, K, X) for the probļem in (a). (d) List the Kunh-Tucker first-order conditions for the problem in (a). (e) Solve the first-order conditions from (d) to find the critical points of the Lagrangian. (f) Justify that the problem in (a) is a concave program and conclude with the values of labor and capital that solve the firm's problem. (g) Based on…Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?11 Q3. y=LAK and (p = $10, w = $5,r= $5). Find the optimal labor and capital, (L", K") to maximize profit.
- Question 28 Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the average fixed cost of producing q units is? AF(q)=3/q. AF(q)=10/q. AF(q)=5/q. AF(q)=1/3q. AF(q)=2/3q.Which of the production function has diminishing marginal returns to labor? (Choose ONE). F(K, L) = K2L³ F(K, L) = KL F(K, L) = K0.10.9 F(K, L) = 2K+ LA firm uses labor (L) and capital (K) to produce rocking chairs (Q) with the following production function Q=LK. The wage (w) is $10 and the rate of capital (r) is $20. The target number of rocking chairs to produce is 800. It is the short run and the amount of K is fixed at 5. What the optimal values for L* and K* in the short run? Enter the number for the the optimal amount of L in the short run? Enter the number for the the "optimal" amount of K in the short run?
- Suppose a firm hires from the competitive labor and capital market to make strawberries. The per unit price of labor is $w and the per unit price of capital is $r. The firm has raised TC amount of seed money and is deciding to allocate it on hiring labor and capital in the least cost way. The production function of strawberries is written as Q = 25LKb which acts as the production target [0A manufacturer named Kjell is facing the following product function.1 x = f(N, K) = 100Nº.8K0,2 The price for labor is NOK 500 per unit. The price for capital is NOK 125 per unit. a) Does the product function provide constant, increasing, or decreasing scale benefits? b) Kjell wants to produce 400 cakes at the lowest possible cost. How much labor and does he need capital? What will be the cost? c) The bank is not impressed by Kjell's production technology. He therefore receives a loan of only NOK 1,875. How many cakes can Kjell produce a maximum of NOK 1,875. d) Make a factor diagram (N, K). Note Kjell's adaptation from problem b) and c). Draw the isocost lines and the substituent template. e) A short-term strike leads to the price of labor rising to NOK 750. Kjell still has only NOK 1,875. How will Kjell change his adaptation from c)?How many cakes does he produce now? f) Kjell eventually starts making money, and wants to expand production to 650 cakes. What will be Kjell's new…Suppose that the production function for Hannah and Sam's home remodeling business is Q = F(L,K) Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places. $ .revised jrl 08-11-2011The marginal product of labor can be determined using the total product of labor curve. Using the equation for the production function, the level of output when L = 8 and K = 25 is (3) 2³. (Enter a numeric response using a real number rounded to two decimal places). q=8LK+5L² Product or Output (q) 3,500- 3,000- 2,500- 2,000- 1,500- 1,000- 500- 0- Production Function 5 2 :8 15 15 10 Labor Input (L) 20 25Suppose that firms face the following production function: Q = LAK^. Suppose also that price of labor (L)=w=3 and price of capital (K)=r%3D9. If the firm wants to produce 120 units of output, what is the optimum amount of labor, capital and associated cost respectively? 60, 60, 120 30, 30, 360 240, 240, 2880 120, 120, 144OSuppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places.SEE MORE QUESTIONS