3. Yasmin (Y) and Xavier (X) run firms that produce goods using capital (K) and labor...
Suppose a firm has a production function given by Q=2K+L, where L is labor, K is capital and Q is the quantity of output. Which of the following statements is WRONG? A. The firm is exhibiting constant returns to scale B. The firm’s marginal product of capital is constant C. The firm’s marginal product of labor is constant D. The firm’s marginal rate of technical substitution depends on the amount of inputs
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor. a. Find marginal product of labor and marginal product of capital.b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.
5. A consumer buys two goods. If the prices of both goods fall by 10% and the consumer's income falls by 20%, then a. the slope of the consumer's budget line will change. b. the consumer's budget line will shift out from the origin with the slope unchanged. c. the consumer's budget line will shift in toward the origin with the slope unchanged. d. the consumer's budget line will not change. 6. The figure at the right shows the isoquant...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
1. Consider the following production function: Q = f(K, L) = (K^1/2) (L^1/2) a) Place capital on the vertical axis and labor on the horizontal axis. Determine the marginal rate of technical substitution. b) Suppose that the price of capital is $10, 000, and the price of labor is $10, 000. What is the ratio of capital to labor that allows the firm to produce any given quantity of output as cheaply as possible. c) Suppose that the price of...
Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor input. Let K>0, L>0. 1. What are the marginal products of capital and labor re- spectively? 2. Please compute the technical rate of substitution (we as- sume K is on the horizontal axis). 3. Dose this production function show diminishing technical rate of substitution (in absolute value) when K increases? Please give a brief proof. 4. Please prove that this production function features increas-...
Let q = L½k½ denote the production function for a firm making long-run decisions, that is K (capital) and L (labor) are now variable. a. Place k on the Y-axis and L on the X-axis and illustrate an isoquant when q=100.b. Derive an expression for the MRTS (the marginal rate of technical substitution) for any level of q.
A farmer uses three inputs to produce vegetables: land, labor, and capital. The production function for the farm exhibits diminishing marginal rate of technical substitution. a. In the short run the amount of land is fixed. Suppose the prices of capital and labor both increase by 5%. What happens to the cost-minimizing quantities of labor and capital for a given level of output? (Remember that there are three inputs, one of which is fixed). b. Suppose only the cost of labor goes...
consider an industry that uses capital, K and labor, L to produce output, X, according to a Cobb-Douglas production function: x=K L where 0 <X<1 is the share parameter for capital and 0<B,1 is the share parameter for labor. Denote the rental price of capital by r and the wage by w. Determine the capital to labor ratio (K/L) wh9ich minimizes the cost of producing a fixed amount of output, X. Under what conditions does optimal ratio of capital to...
1. A country's resources (land, labor, and capital) are used to produce the goods and services that satisfy the wants of its population. For each of the following, identify whether it should be classified as land, labor, or capital and justify your conclusion. Remember to consider the economic use of these terms (i.e. land, labor, and capital). a four year college degre a. b. the software used to make Facebook available to users c. 100 shares of Microsoft stock d....