The firm Greench produces Nutella. The production function is given by the following: Nutella = min{ 44 L, 27 K} The price of labor is $36, the price of capital is $10, the price of Nutella is $25, and Greench's costs are $3607. What is the optimal amount of labor that the firm should hire?
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- Tom Petersen is considering renovating bar stools at Dreamland. The productionfunction for new bar stools is given byq= 0.5L0.5where q is the number of stools produced during the renovation week and l represents thea number of worker hours employed during the period. The firm is a price taker for both bar stools(which sell for P) and workers (which can be hired at a wage rate of w per hour).a. What is the cost function for this firm C(w,q)?b. What is the supply function for bar stools q(P,w)?c. What is the profit function for this firm (P,w)?d. What is the firm’s demand function for labor function L(P,w)?Please explain what numbers are being plugged in to get the answer.A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q). (d) Suppose wL = $25 and wM = $2. Determine the cost-minimizing combination of inputs if the baker wants to produce 200 mules. (e) Using wL = $25 and wM = $2 and the demand functions from part (c), write the firm’s long run cost function CLR(q).
- 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.Assume that the above data are for Ali's Surfboards firm which hires workers at $500 a week and its total fixed cost is $1,000 a week.Calculate APL,MPL, AVC, AFC, AC, and MC of each output in the table, ( Values are given for L=1, you are asked to do the rest up to L=7).Labor Output APL MPL AVC AFC AC MCHomer's Donut Shoppe has the production function q=10L +20L²- 5L³. The marginal product of labor is A. MP = 10 + 20L B. MP = 10 + 20L - 5L² C. MP=10L D. 2 MP=10 + 40L-15L
- Suppose Die Cast Aluminum Co. is a subcontractor for the auto industry and makes specialized auto parts. There is a bracket it manufactures that it sells for $2.00. The following table shows the number of brackets that can be produced from a given number of labor hours. Assume that the company cannot hire labor for a fraction of an hour. Hours of Labor Output 1 50 2 90 3 120 4 140 5 150 155 157 6. The marginal product of labor for the first hour of labor is || (Enter your response as an integer.) The value of the marginal product of labor for the first hour of labor is. (Round your response to two decimal places.) If the wage paid to workers in Die Cast's plant is $25/hour, it should employ worker(s). (Enter your response as an integer.) If the wage paid to workers in Die Casť's plant is $35/hour, it should employ worker(s). (Enter your response as an integer.) If the wage is $25/hour, but the price of a bracket declines to $1.50, it should employ worker(s). (Enter your response as an…Consider the production function of the firm below. Which of the following is NOT true? The marginal product of labor at B is 70 units. The total product is increasing as inputs to production increase. The marginal product of capital at point D is 50. The marginal products of both labor and capital are always increasing.Consider the following diagram showing a range of isoquants and isocosts, with labour measured on the horizontal axis and capital measured on the vertical axis. Assume that when the firm is producing in the short run, capital is fixed at K but capital is variable in the long run. K, Capital K A B Q3 Isoquant Q2 Isoquant Q₁ Isoquant L, Labour Which of the following can we conclude? O Only point B represents cost minimisation in both the short run and the long run, as it is on the short run expansion path, as well being the cost minimising point in the long run. Points A, B and C represent cost minimisation in the long run only. There are no points that represent cost minimisation in both the short run and the long run. Points A, B and C represent cost minimisation in both the short run and the long run. Points D and E represent cost minimisation in the short run only. Points A, B and C represent cost minimisation but only in the short run. Points D and E represent cost minimisation in…