A computer assembly firm’s production function is q = 0.1L (K) + 3L (2 K) - 0.1L (3 K). a) What is its short-run production function if capital is fixed at K = 10? b) Give the formulas for its marginal product of labor and its average product of labor

Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.

A firm's short-run production function is displayed in the figure below. The firm's variable input is labor. Assume that when Əq (L) 4 units of labor are being used, the slope of the short-run production function reaches its maximum value of 7 (i.e. ƏL 7 when L = 4). As the level of labor increases beyond L = 4, the short-run production function is always becoming less Əq (L) steep (i.e. it is concave). The slope of the production function is equal to 5 when L = 5 (i.e. = 5 when L = 5). If 6 units ƏL Əq (L) of labor are being used, the slope of the production function is 3 (i.e. = 3 when L = 6). If the firm has to pay a wage ƏL of $15 (w = 15) for each unit of labor and can sell each unit of output at a price of $3 (p = 3), what is the firm's profit- maximizing level of output (q) in the short-run? 9₁ 18 14 8 0 4 5 6 q(L) L 7 / 8

Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a)  Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b)  At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c)  Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d)  Does this production function exhibit constant, increasing or decreasing returns to scale?

Suppose Z=0, Y=9. Please solve in details.

Given the following production function: q = 10KL. Assume that w = 25, r = 75 and C = 1200. (a) Mathematically find the minimum cost combination of capital and labour to produce a given level of output.b) Does the production function in part (a) show increasing returns to scale, decreasing returns to scale, or constant returns to scale? Explain.  (c) Using isoquants and isocosts, graphically illustrate the effect of an increase in the wage rate, assuming the firm is producing at the same level of output.

Which of the following production function would exhibit increasing returns to scale? f(K, L) = (K+ L)1/2 f(K, L) = K + L f(K, L) = K1/4+ [1/4 Of(K, L) = KIL None of the above

A firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew Select one: O a. is vertical. b. is horizontal. c. is a ray through the origin with slope 3. d. is a ray through the origin with slope 4. O e. has a negative slope.

Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?

Suppose a firm could produce data storage services using two inputs: high capacity hard drive (200 TB) or low capacity hard drive (100 TB).   What is the production function and what is a typical set of isoquant?