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- Suppose the short-run production function is q = 11L². Suppose that the wage rate is $112 per unit of labor. What is the marginal cost at q = 255?The production function for a firm is: q=-0.6L3+18L2K+10L where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. b For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. Hint: you will not be able to solve the total product curve for L as a function of output. So, instead construct a table, See the headings. Use this definition ΔTC/Δq…Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of managers decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition?
- Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is constant at $20/unit. The production function and marginal product function, respectively, are shown below. If the current capital stock is fixed at 2,500 units, how much labor should the firm employ in the short run? Show your work.The production function for a firm isq=−0.6L^3+18L^2 K+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period.a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL.MPL=−1.8L^2+36L+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.I am having trouble finding out the formulas to complete this question: The production function for a firm is q = -0.6L3 + 18L2K + 10L where q is the amount of output, L is the number of labor hours per week, and K the amount of capital. The wage is $100 and the rental rate is $800 per timeperiod. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. You will not be able to solve the total product curve for L as a function of output. So, instead construct a table. Headings: L q(L) APL MPL VC TC AVC AC MC w/APL w/MPL
- A firm produces output that can be sold at a price of $10. The production function is given by Q = F(K, L) = K1/2 L1/2 If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?For a short run production function q=10lnL if L=5 and wage 3, more workers will be hired if the price at which the output can be sold is more than.......Q9 Suppose capital costs $10 per unit and labour costs $5 per unit. For a profit-maximising firm operating at its optimal factor mix, if the marginal product of capital is 50, then the marginal product of labour must be... a. 25. b. 50. c. 100. d. 20. e. 10.
- The firm aims at maximizing its profits in the short run. The wage level is w=140. The production function is as below. Variable Input (Labour) Price of output Output L P Q 0 5 0 1 5 58 2 5 112 3 5 162 4 5 208 5 5 250 6 5 288 7 5 322 8 5 352 9 5 378 10 5 400 11 5 418 What is the optimum number of workers? a. 3 b. 4 c. 5 d. 6 e. All the other answers are wrong.The production function for a firm is q=−0.6L^3+18L^2 K+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period.a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. MPL=−1.8L^2+36L+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with q
