Consider an economy where the production function is Y = K L¹, with a 0.75. Suppose this year there are 625 units of capital and 4096 workers. What is the marginal product of labour? O 1.265 0.469 00.4 O 1.2 0.061
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- Consider the augmented production function Y equals A K to the power of 1 divided by 3 end exponent open parentheses H N close parentheses to the power of 2 divided by 3 end exponent, where Y is output, A is total factor productivity, K is capital, N is the number of workers, and H is average years of education. Suppose that A=2, K=8, and N=1000. What is the average product of labor (or output per worker) if H is 15.7?This problem is connected to module 10. Again, its purpose is to acquaint you with the summary measures of production theory, and to reason about production theory. In the short run, a firm cannot vary its capital and operates with K = 9. It can, however, vary the amount of labor (L) that it uses. For each production function below, explain why the firm will or will not experience diminishing marginal returns to labor in the short run. q= 35L + 40Kq= (L^0.5)(K^0.5)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 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.Let a firm's production function Q (L)=12L^2-1/20L^3 (i.e. output as TL orthe amount of production depends on the workforce, L, as Q is the number of people with a single production input). This functionlet be the foreground 0 ≤ L ≤ 200 for. Accordingly,A) What is the number of labour force (L*) that will make output (Q) the highest?B) what is the number of workers (L**) who will make the maximum amount of output per employee(i.e. Q (L)/L)?c) in both cases the output of the L* and L** values you find and the output per employee at the mosthow can you be sure it's high? Show me.Assume that the production function of a firm is Q = L0.23K0.10. L = labor, K = capital.Referring to the information given,i. Calculate the technical suit replacement rate (MRTS) of the firm? ii. Calculate the value and explain the form of return according to the scale (return to scale) of the firmthe?
- You are given the production function: Q(k,L)=10KaLB a) What is the average product of labour, holding capital fixed at K? Simplify fully b) What is the marginal rate of technical substitution (MRTS)? Simplify fully Does the above function exhibit increasing, decreasing or constant returns to scale? Illustrate why and explain what this means10. If over the range of positive marginal product, the short-run total product of factor A in the production of X is given by the equation: X=aA +b A2 – A3 Where a, and b are positive constants, and if the average product of A is maximized when X=100, then the marginal product of A must be greater than the average product when X=50. True or False ?. Prove your answer.Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK1/3 L2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. D) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so.
- The firm employs workers for R100 per day. Each unit sells for R30. The firm’s production function is as follows: Labour Output 1 6 2 11 3 15 4 18 5 20 6 21 Q3.2.1 Re-draw the table above and add two columns one showing the Marginal Physical Product and the other column showing the value of the marginal product of labour MRP) at each input level.Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK^1/3 L^2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. d) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so. E) Suppose that the quantity of capital K doubles as well. (So now both K and L aretwice their previous value). Calculate Y, w, r, Y/L, and K/L. Comment on how thesenumbers changed relative to both their initial values, and their values in (d).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?
