Q7. The production function is y=L¹/aK¹/B. $12. The price of the output is $100, w = $15, and r=; a. Find the optimal input of labor and capital. b. Find the optimal output which maximizes the profit.
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- A 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?Consider the table below that describes the production function for a good (Q) in terms of inputs labor (L) and capital (K) in the short run.Con Co. produces a collectible card game. Currently, the price of capital is at $50 and the price of labor is at $10. The marginal product of capital is 200 and the marginal product of labor is 30. To minimize cost of the given output, Con Co. should Use more capital Use more capital and labor Leave capital and labor as is Use more labor
- Economics Suppose that firms face the following production function: Q = L + K + 2L ^ (1/2) * K ^ (1/2) This production function exhibits information that is not enough to determine Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale Constant Returns to ScaleWhich of the following represents the optimal combination of Capital and Labor under the goal of cost minimization in the long run? [MR=Marginal Revenue, MC=Marginal Cost, MPL=Marginal Product of Labor, MPK=Marginal Product of Capital, K=Capital, L=Labor, PL =Price of Labor, PK =Price of Capital] DK/DL = MPL/MPK MR > MC MPL/PL= MPK/ PK MPL = MPKDoes optimal use of an input (such as labor) mean maximizing average output (per unit of input)? Explain.
- Which of the following is a cause of diminishing marginal productivity? a.In the long run, labor gets tired as more labor gets added to the production process. b.In the short run, labor runs out of available capital as more labor gets added to the production process. c.In the short run, capital gets more expensive as you add more capital to the production process. d.In the long run, capital depreciates as more capital gets added to the production process.Which of the following statements best describes a production function? Group of answer choices all levels of inputs that could produce a given level of output the maximum profit generated from given levels of inputs the maximum level of output generated from given levels of inputs all levels of output that can be generated from given levels of inputsQ87 Consider a firm that uses only labour and capital as inputs. At the present use of labour and capital, the MP of labour is four times the MP of capital and the price of labour is twice the price of capital. To minimise its costs for a given level of output, the firm should... a. Decrease both capital and labour. b. Increase both labour and capital. c. Decrease capital and increase labour. d. Stay at its present factor mix. e. Decrease labour and increase capital.
- The production function of a firm is f(x, y) = x + y. The marginal product of input xdiminishes with an increase of x.• True• False Please explain!Consider the table below that describes the production function for a good (Q) in terms of inputs labor (L) and capital (K) in the short run. What is the marginal product of labor for the fourth worker? Enter the number below.What is the optimal combination of Capital and Labor under the goal of cost minimization in the long run? [MR=Marginal Revenue, MC=Marginal Cost, MPL=Marginal Product of Labor, MPK=Marginal Product of Capital, K=Capital, L=Labor, PL =Price of Labor, PK =Price of Capital]