What is the elasticity of substitution for the production function f(K, L) = K2 + L2? O b. o = %3D O c. o = 1 O d. o = 2 O e. o = 4 Clear my choice A firm's cost function is C(q) = 2000 + 10g + 5q². If the firm is a price-taker in a market that is in long-run equilibrium, what quantity does the firm sell? %3D O a. q = 5 O b. q = 10 O c. q = 20 1/14
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- A firm is currently producing 500 units of output daily by employing 60 units of labor daily at a price of $10 per unit and 30 units of capital daily at a price of $20 per unit. The marginal product of the last unit of labor employed is 3, and the last unit of capital employed is 5. a. Given the above information, what does the firm's marginal rate of technical substitution, MRTSL,K, equal? b. Indicate on the following diagram some point labeled A that is consistent with the information given in the question.A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (a) Prove that this production function has decreasing returns to scale. (b) Find the optimal (cost-minimizing) ratio of capital to labor inputs K L for any level of output (use scale expansion path). (c) For any q, nd the cost minimizing inputs as functions of output: i.e., derive functions L(q) and K(q).The marginal rate of technical substitution of L=2K means that the firm can substitute 2 units of capital for an additional 1 unit of labor in the market. True or false.
- Consider the production function Q = 2(KL)0.5 What is the marginal product of labour and capital What is the marginal rate of technical substitution of labor for capital What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit?Consider a production function in such a form: Q= f (K,L)= 3KL Calculate the elasticity of substitution (Ϭ) for this firm.Consider the following short-run production function (where L – labour, Q - output): Q = 10L - 0.5L^2Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input as it needs at $20 per unit.Determine the marginal value of product with respect to labour.Determine the marginal cost of labour (factor cost function).Determine the optimal value of L, given that the objective is to maximize profits.
- A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization 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.Assume that the production function for competitive firm is given by F(L)=9L1/3, where L is the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?y= f(x1,x2)=x1ax2b If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output. Redo part (1), this time by first deriving the firm’s conditional factor demand functions and the cost function.
- Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners’ time (T). The shop’s productionfunction is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P perunit, and the owner’s time costs $1 per unit.a. Write down Needful Things’ profit function.b. Suppose in the short run, the owner’s time is fixed at T=16. Find the first order condition for the short-runprofit maximizing amount of labor.c. Solve for the amount of labor that the shop uses in the short run to maximize profit as a function of P. Is youranswer consistent with the law of demand? Explain. d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizingamounts of both inputs. e. Solve for the amount of labor and time that Needful Things uses to maximize profit in the long run.The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) ina very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital isrented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production isGH¢1,000. Suppose the firm’s production function (Q) is as follows:? = 14?0.5?0.5 + 10Determine the optimal input usage and the maximum profit.Suppose that a firm has production function F(L, K) = L2/3 K1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.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.