Suppose the production function is given by Q= 5K - 2L. What is the marginal product of the 6th capital when 5 units of capital and 10 units of labor are employed? A.5 b. 4 c. 11 d. 45
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- Assume labor (L) is the only variable input used in the production process, a firm’s production function is given by Q=7L+10L2-L3 where Q represents total product. Classify the production function in to the three stages of production.F (L, K) = L0.2K0.7， The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L,K) = (1,1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination?A firm's production function is: q = 20L1/2K1/2 where q is the firm's total product, L is the quantity of labor employed, and K is the quantity of capital employed. The price of labor is $25 per unit and the price of capital is $100 per unit. a. What is the equation for the marginal product of labor? b. What is the equation for the marginal product of capital? c. Given the price of labor is $25 per unit and the price of capital is $100 per unit, what is the cost-minimizing combination of capital and labor that can produce 800 units of output?
- compute the marginal product of capital (MPK) and the marginal product of capital (MPL) of b. Q=K2/ 5L3 /5Suppose a firm producing metal rods in the short run faces a production function of the form. Q = 100K2L2 – L3K3 If capital is fixed at 10 units i. Computing the appropriate concept, explain the consequences on production if management was to allow two additional workers to be employed. ii. How many metal rods are produced when the Average product of labour reaches its maximum? iii. Comparing the average level of productivity between parts (i) and (ii) above, which has the higher level and why?#4a.Suppose A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is:X=-0.2L3 + 18L2 + 1620L.Where X is the number of units of the product per week, and L is the number of persons employed.A. A t what weekly output is marginal cost equal to average variable cost?B. if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?.
- A firm engaged in the manufacture of RTWS faces the short-run production function Q = 250L - 5L², where L is the number of units of labor and Q is the number of RTWs produced annually. d.) How many RTWS can be produced by the firm in a year if there are 10 units of labor? e.) Compute the marginal product of the 40th unit of labor. f.) How many RTWs can be produced by the firm in a year if there are 40 units of labor? g.) Sketch the graph of the production function.Suppose that the production function is given as follows:TPL = 10L + 5L2 + L3Find the total product, Marginal product and average product when L = 5.The manager of Dixie Furniture Company estimates that the daily output of her factory (in thousands of dollars) Q is given by Q = 2x1/4y3/4 where x is the amount spent on labor and y is the amount spent on capital (both measured in thousands of dollars). (a) Find the daily output of the factory if $81,000 is spent on labor and $256,000 is spent on capital each day. $ (b) Suppose that the output of the factory is to be maintained at the level found in part (a). By how much should the amount spent on capital be changed if the amount on labor is increased by $1,000? (Use the differential to calculate the answer. Round your answer to the nearest cent.) $ What is the MRTS? (Round your answer to the nearest cent.) $ per thousand dollars
- 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.A firm produces output according to a production function: Q = F(K,L) = min {4K,8L}. a. How much output is produced when K = 2 and L = 3? 192 Numeric ResponseEdit Unavailable. 192 incorrect.unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: 80 Numeric ResponseEdit Unavailable. 80 incorrect. Labor: 480 Numeric ResponseEdit Unavailable. 480 incorrect. c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour? multiple choice Capital and labor increase. It does not change. Capital increases and labor decreases. Incorrect Capital decreases and labor increases.A19 Subject - economics Consider a constant returns-to-scale production function f(k, l). Show that f(k, l) = k ∂f/ ∂k + l ∂f /∂l