1. Suppose a short-run production function is described as Q = 40L 0.04L2 where L is the number of labors used each hour.

2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 3 8 12 15 17 K=2 10 15 19 22 24 K=3 16 21 25 28 30 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L?

Consider the production function from earlier: Quantity of Haircuts 20 15 10 0+0 0 N 2 8 14 O Increasing marginal productivity O Constant marginal productivity O Decreasing marginal productivity 3 19 23 Labor (hours) 27 26 Total Product Curve From 1 labor hour up to 7 labor hours, what sort of marginal productivity does this production function have?

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.

5. Selpats produces pens with the production function f(k, l) = 200vkl. The price of capital is wk = 40 and the price of labor is wL = 10. (i) Determine the optimal input bundle for producing y pens in the long run and find the long-run cost function. (ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run. (iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run total cost function and the short-run marginal cost function. Explain the relationship between the short-run and long-run marginal costs when y = 10,000. (iv) Suppose that the price of output is p. Which value of y maximizes short-run profit? р.

Suppose a firm's production function is Q=200L +5L2-0.08L³. Which of the following is the Average Production of Labor (APL)? Oa. 200+10L-0.24L² Ob. 10L-0.24L² Oc. 5L-0.08L² Od. 200+5L-0.08L²

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Suppose the production function for T-shirts can be represented as q =  L0.25 K0.75. Show that the production function has constant returns to scale.

A firm estimates its long-run production function to be Q = -0.0050 K³L³ + 15 K²L² Suppose the firm employs 10 units of capital. At product of labor begins to diminish. A) 150 B) 66.67 C) 1000 D) 100 E) 200 I units of labor, marginal

In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the cost of labor is £4 per unit and the cost of machines is £4 per unit, what is the short-run total cost of producing 48 units of output? Use Lagrange