2. Suppose a production function is q = K1/21/3 and in the short run capital (K) is fixed at 100. If the wage is $10 an rental rate on capital is $20, the short run production function is a. q = 10L 1/3 1/3 b. q = 100L C. 1 9 = 11/3 d. q 10 = 100
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- 2. Suppose a production function is q = K¹211/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20, the short run production function is a. q = 10/¹/3 b. g=1002¹/3 C. 1 q= = -11/3 10 d. g = 100= $30 and wage rate Let the production function be given by: q = 10(L^2)K, with rental rate v W = $20. 1. How much K and L are employed to produce 11,250 units of output? 2. Suppose that the firm wants to increase output to 19, 440 units of output, now how much K and Lare employed to produce with minimize cost? 3. Suppose that in the short run the amount of capital is fixed at K = 10, what is the firm short run fixed cost? 4. Suppose that in the short run the amount of capital is fixed at K = 10, what is the short run total cost of producing 900 units of output?5. Suppose the production function is given by f(E, K) = E'/³K²/3. The hourly wage rate is $2 and the price for a unit of capital is $32. The output level is ĝ = 144 and the price of the output is $30. (a) Write a firm's CMIN problem. (b) Impose FONC to find MP(E) = w and MP(K) = r. %3D
- 1) For the following functions of production, find the functions of conditional input demand and the cost functions a. q = A min(az,, bz2}; b. q = Azf z; C. q = azı + bz2 d. q = az, + b(lnz2) a, b > 0 A, a, b > 0 A, a, b > 0 a, b > 0 2) For A and D of Point 1, verify Shepard's lemma. 3) For B demonstrate that is possible to retrieve the supply function based on what has been developed so far, in this case, atb<1 www.2 Suppose that production for good X is characterized by the following production function, O = K0.5L0.5 where Kis the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the fixed cost of using 81 units of capital and 9 units of labor is: a. $135. b. $2,025. c. There is insufficient information to determine the fixed costs. d. $2,160.Suppose a production function is q = K1/2L1/3 and in the short run capital (K) is fixed at 100. If the wage is $10 and therental rate on capital is $20, the fixed cost isa. $2,000b. $200c. $20,000d. $0
- Question : Suppose a firm has a production function Q = 10VKL so that 5/K MPL 5/L VK MPK The firm uses 9 units of capital in the short run: K = 9 The wage is $80 and the rental rate of capital is $5 What is the cost of producing 60 units of output? $445 $108 $365 $276Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where k represents capital and l represents labora. a. Show that MPk = (q/k)1 and MPl = (q/l)1 . b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ). c. Determine the output elasticities for k and l; and show that their sum equals 1.Note: Output elasticity measures the response of change in q to a change in any input. Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)1/3 1/3 Badgett's Gadgets produces gadgets with the production function, y = x, where x1 is the quantity of labor input, 2 is the quantity of capital input, and y is the 1/3 quantity of output. In the short run, Badgett's capital input is fixed at x=8, and so its short run production function is y = 3(8)¹³ = 2z/³. The per-unit price of labor input is w₁ = 20 and the per-unit price of capital input is w₂ = 40. If Badgett's is a price taker in the output market and can sell as many gadgets as it wishes at a per-unit price of p, what is the lowest value of p at which Badgett's is able to earn positive profits in the short run? Badgett's will earn positive profits for any p > 40. Badgett's will earn positive profits for any p > 80. Badgett's will earn positive profits for any p > 0. Badgett's will earn positive profits for any p > 120.
- A firm's production function is: q = 16L1/2K1/3 where q is the firm's hourly total product, L is the quantity of labor employed, and K is the quantity of capital employed. Assume that the quantity of capital employed is fixed at 125 units per hour. The labor market is perfectly competitive, and the current wage, w, is $10 per hour. The firm sells its product in a perfectly competitive market and the price is $5 per unit. a. What is the firm's value of marginal product of labor? b. What is the firm's profit maximizing quantity of labor?2. A firm has a production function of q = 0.25KL0.5 and in the short-run capital is fixed at 100 (K = 100). %3D The rental rate of capital = = $100. r The wage rate = w = = $25 а. Write the equation for the short-run production function. b. What is the firm's short-run demand for labor (L as a function of output)? What are the equations for the firm's short-run total costs (TC as a function of q), short-run average total costs (ATC as a function of q), and short-run marginal costs (MC as a function of q)? а.A firm is currently producing such that: MPL = 30 W = 10 MPK = 20 To minimize the cost of production, this firm should: a. Use more labor and less capital which will (likely) decrease the MPL b. Use more labor and less capital which will (likely) increase the MPL C. Use less labor and more capital which will (likely) decrease the MPK Od. Use less labor and more capital which will (likely) increase the MPK v = 20