Consider the following production function: Assume capital is fixed at K = 25. At what level of employment does the marginal product of labor equal zero? The marginal product of labor equals zero when
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- Consider the following production function: q = 32LK + 10L2 - Assume capital is fixed at K= 25. At what level of employment does the marginal product of labor equal zero? The marginal product of labor equals zero when (Enter a numeric response using an integer.) Beyond a labor input of 40, the marginal product of labor is 20 étv MacBook Air DI DD F3 F5 F6 F7 FB F10 FW 2# $ & 3 4 5 8 9 E R Y P D F G н J K C V B N M command VA firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labour is maximized? How many persons are employed if the marginal physical product of labour is maximized? What is the quantity of X when average variable cost is minimized? If the weekly wage is $360 and the price of X is $30 per ton, how much X should be produced to maximize profits?A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labor is maximized? How many persons are employed if the marginal physical product of labor is maximized? What is the quantity of X when the average variable cost is minimized?
- Suppose the production function for widgets is given by q=KL+6L²-0.1L³ where q represents the annual quantity of widgets produced, K represents annual capital input and L represents annual labor input. A) Suppose K=10. At what level of labor input does average product of labor reach a maxiumum? How many widgets are produced at that point? B) Again assuming that K=10, at what level of labor input does MPL=0? C)Determine and show whether the production process exhibits law of diminishing returns.For the production function Qs = K0.4L0.8 in the short run, where capital is at 620 find the marginal product of labor at L = 78. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).Consider the production function q=5L^(0.3) K^(0.5) The marginal product of labor is MPL=1.5L^(-0.7)K^(0.5) Assume that capital is fixed at K=9 in the short run. Derive the formula for the short-run total product and graph it. (Hint: Substitute in the production function
- Suppose the production function for widgets is given by q=kl -0.8k²-0.21² where q represents the annual quantity of widgets produced, k represents annual capital input, and I represents annual labor input. Suppose k = 10; at what level of labor input does this average productivity reach maximum? (please put your answer in numerical values with no comma or decimal place). How many widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 10, at what level of labor input does MPL = 0? Suppose capital inputs were increased to k = 20, at what level of labor input does this average productivity reach maximum? widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 20, at what level of labor input does MPL = 0? answer in numerical values with no comma or decimal place). Does the widget production function exhibit constant, increasing, or decreasing returns to scale?…QUESTION 1 For the production function Qs = K0.6L0.5 in the short run, where capital is at 307 find the marginal product of labor at L = 68. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).Suppose that a firm's production function is given by the following relationship: Q = 2.5√/LK (i.e., Q = 2.5L0.5 K0.5) where is output, L is labor input, and K is capital input. What is the percentage increase in output if labor input is increased by 10%? (Assume that capital input is held constant.) What is the percentage increase in output if capital input is increased by 25%? (Assume that labor input is held constant.) What is the the percentage increase in output if both labor and capital are increased by 10%? 11
- Question 3: Consider the following production function: Q = ALa K¹. Assume A > 0. Further assume 0 < a < 1, and 0 < b < 1. 1. What is the Marginal Product of Labor (MPL)? Is it diminishing as L increases? What is the Marginal Product of Capital (MPK)? Is it diminishing as K increases? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (APK)? 3. What is the TRSL,K? Is the absolute value of TRSL,K diminishing in K? Is it diminishing in L? 4. Are there constant, decreasing, or increasing returns to scale? How does this depend on the parameters?Suppose that the production function for compact disc player is Q=100L 0.6K 0.4 Where ? is the total output, ? is the quantity of labor employed, and ? is the quantity of capital in place. a) Calculate TP, AP, and MP for the sixth, seventh and eighth units of labour employed if capital is fixed at 240units.A cob Douglas production function for a firm is given as Q=4L ½K½. The firm has also established that wage rate and interest paid on capital are $3 and $5 respectively for a production period. The firm intents to spend $200 million for the period on production cost. Compute the levels of capital and labor that will maximize output. What is the maximum output?