A country's Cobb-Douglas production function is as follows: Y= 5K^(1/2)L^(1/2). If this country has 15,000 unit of capital and 600 workers, find the real wage approximately. Select one: a. 16.36 b. 9.12 C. 15.81 d. 6.45
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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?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?10. 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.
- Given the Production function for Mwaba & Mutale Enterprises as follows: Q = f (k,l) = 300k 2l2 - k 3l3, Assuming the value of K is 5, Determine the value of L, for which APL is maximum Prove that at the point where MPL is equal to APL , APL is maximum. The value of labor input L, for which output is maximum Total output at this value of labourSuppose a firm has a Cobb-Douglas production function given by: Q = A * L^0.5 * K^0.5 If the firm currently employs 100 units of labor and 64 units of capital and produces 500 units of output , can you calculate the value of the total factor productivity for this firm?Given the linear production function: Log (Q) = 1.5 + 0.76 Log (L) + 0.24 Log (K) Where Q is the level of output, L is the units of labor and K is the units of capital employed. a. If one worker's wages are $30 per day, how many workers should the firm employ per unit of output? b. What is the percentage of the firm's revenue spent on labor?
- Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.Suppose that a unit of capital costs three times as much as a unit of labor.If a firm currently has a technology such that MPK =50, MPL =30, how should this firm adjust its capital and labor choices?Holding the output of stereo sets constant, a large increase in the use of the input capital will cause the labour input to increase proportionately to capital. True or False?
- in an economy with production function Y = 1.5 × K^0.3L^0.7, K = 343, and L = 512. If factor markets are in equilibrium, then the rental price of capital is (approximately) ________, and the real wage is (approximately) ________. A) 0.5; 0.8 B) 7; 8 C) 0.9; 1.35 D) 1.4; 0.4 E) 0.6; 0.9A 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.Suppose there are two primary factors of production, labour (L) and capital (K), and there are nosecondary factors of production. The production function for this economy is simply Y = cKL,where c is a constant and α= 0.5. Which of the following is true? 1.This economy exhibits constant marginal product of labour 2.This economy exhibits decreasing returns to scale 3.This economy exhibits constant marginal product of capital 4.This economy exhibits diminishing marginal product of labour