2. Suppose a producer's production function is F(X,L) = 3KL The cost of K is 20 (r=20) and the cost of L is 80 (w = 80) The finn wants to produce 30 units of output. a. What is the cost-minimizing way for the firm to produce 30 units of output? How many units of capital and how many units of labor should be used? b. Suppose the firm has committed itself to 4 units of capital (K) and therefore is operating in the short run. What combination of inputs is the least costly way for it to produce 30 units now?

2. Suppose a producer's production function is F(X,L) = 3KL The cost of K is 20 (r=20) and the cost of L is 80 (w = 80) The finn wants to produce 30 units of output. a. What is the cost-minimizing way for the firm to produce 30 units of output? How many units of capital and how many units of labor should be used? b. Suppose the firm has committed itself to 4 units of capital (K) and therefore is operating in the short run. What combination of inputs is the least costly way for it to produce 30 units now?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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part D E F
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.
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?
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Problem 7. A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q 20KL The price of one unit of capital per hour is $20 and the price of one unit of labour per hour is $20. You have been instructed to have a total cost of $1,000 or TC $1,000. Find the optimal amount of labour and capital that you will be using, and compute the amount of output..
Suppose that a firm's production function is: a = 3L * K ^ 0.5 The cost of capital is $30/unit; the cost of labor is $20/unit. What is the minimum cost of producing q = 243 ?
Q2) Distinguish between economies of scale and economies of scope. Why can one be present without the other?
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Consider a production process where flowers are grown (the output) using gardeners (labor) and greenhouses (capital). The quantity of flowers grown per day with various combinations of labor and capital are shown in the table below. Suppose that each gardener is paid $200 per day and the greenhouse is rented for $500 per day. Fill in total cost in the table below. (Enter your responses as integers.) Labor Capital Output Total Cost 0 1 0 $ 1 1 160 2 1 480 3 1 640 4 1 720 5 1 760
can you explain how they got M=y^2/2 and L=2y^2 from part b of this question
3. Frisbees are produced according to the production function q = 2K+L where q = output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for frisbees becoming q = 3K+ 1.5L. Answer part a through part d for this new production function and discuss how it compares to the previous case.