6. A plant's production function is Q(L,K) = 2KL + K. The price of labor services, w, is $4, and the price of capital services, r, is $5. In the short-run, the plant's capital is fixed at K = 2. The firm must produce 40 units of output. How much money is it sacrificing by not having the ability to choose its level of capital optimally? That is, how much more does it cost to produce 40 units of output in the short-run compared to the long-run? (Hint: After setting up the tangency condition, solve for L instead of K before plugging into the production function. The math will be easier since L only enters the production function once!) (See Besanko Problem #7.28) a. $38 b. $10 c. $9 d. $28 е. none of the above

6. A plant's production function is Q(L,K) = 2KL + K. The price of labor services, w, is $4, and the price of capital services, r, is $5. In the short-run, the plant's capital is fixed at K = 2. The firm must produce 40 units of output. How much money is it sacrificing by not having the ability to choose its level of capital optimally? That is, how much more does it cost to produce 40 units of output in the short-run compared to the long-run? (Hint: After setting up the tangency condition, solve for L instead of K before plugging into the production function. The math will be easier since L only enters the production function once!) (See Besanko Problem #7.28) a. $38 b. $10 c. $9 d. $28 е. none of the above

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1
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.
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KA. A firm produces output with the production function, Q = F(K, L) = K0.5 L0.5 with r=4 and w= 2. The firm is using K=16 and just enough L to produce 16 units of output in the short run. How much could the firm save if it were producing 16 units in the long run?
With a production function like Y=zN, which of the following must be true at the optimum? A).The marginal product of labor is smaller than real wage. B).The marginal product of labor is bigger than real wage. C).The representative firm makes positive profits. D). Profits of the representative firm are zero.
14. A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm's production function is: X=-0.2L + 18L? + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A. At what weekly output is marginal cost equal to average variable cost? B. if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?
Consider the production function of the firm below. Which of the following is NOT true? The marginal product of labor at B is 70 units. The total product is increasing as inputs to production increase. The marginal product of capital at point D is 50. The marginal products of both labor and capital are always increasing.
Question 6 Profit maximization A firm faces the following production function q = 100L0.6K0.6 The wage rate, w, is $4.00 and the price of capital, r, is $2. 1. If the firm uses 100 units of capital how much labor should it use to minimize costs? 2. Does this production technology exhibit increasing, constant, or decreasing returns to scale? Why?
Consider a short run production function q = cL+K where the value for c=3, using L units of labour and K units of capital. a) Compute the marginal product of labour. b) Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.
Ma4. A firm produces output with the production function, Q = F(K, L) = K0.5L0.5 with r=4 and w= 2. The firm is using K=16 and just enough L to produce 16 units of output in the short run. How much could the firm save if it were producing 16 units in the long run?
Suppose the representative firm of the economy has a production function of the form F(K, N) = AKO.5N 0.5 The marginal product of labor is then given by MP N = 0.5AK0.5N –0.5 . The current capital 3. stock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some important features of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w)= 10. What is the equilibrium wage w, employment level N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w, employment level N, and full employment output Y ? (e) Depict this change graphically. Denote the original labor supply and demand curves by NS and ND respectively. Denote the new labor demand curve after the productivity shock by ND' . (Does not need to be to scale).
Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.