ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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- The following table shows the capital and labor requirements for 10 different levels of production. Assuming that the price of labor (PL) is $8 per unit and the price of capital (PK) is $6 per unit, compute and graph total cost, marginal cost, and average cost for the firm. To do this, fill in the total cost for each output level in the table below. (Enter your responses as whole numbers.) 9 0 1 2 3 4 5 6 7 8 9 10 K 0 20 20 20 20 20 20 20 20 20 20 L 0 3 7 10 13 17 23 31 41 53 67 TC 0 Cost per unit ($) 0 1 2 3 4 5 6 7 8 9 10 11 12 Units of output Q ✔arrow_forwardSuppose the production of Scooby Snacks at x units of labor and y units of capital is given by the Cobb-Douglas production function P(x, y) = kx"y" where m, n, k are known positive constants and m+ n = 1. The company can spend only p dollars for the production of Scooby Snacks. The cost of one unit of labor is b dollars, while the cost of one unit of capital is c dollars. Using Lagrange multipliers, find an expression for x and y where maximum production will occur?arrow_forwardIf a firm has 5 units of capital, 10 units of labor, and the production function is Q = 4L + 3K what is the Marginal product of capital? 3 4 11 45arrow_forward
- Seton is interested in reducing costs while maintaining quality and patient satisfaction. You have been hired by the Seton Hospital System to improve efficiency. In particular, Seton believes that it is not efficiently combining physician labor hours (L) and physical capital units (K) in producing stent surgeries. Assume that we know that the production function is Q = KL. Assume that the price of L is $1/hr and the price of K is $4 per unit. a. How might Seton use more capital and less labor to install the same stent? What does that real-life tradeoff look like? b. We are going to find the cost minimizing way of producing 100 stent surgeries at Seton. Begin by drawing yourself a picture of how you will solve this problem. Place K on the vertical axis and L on the horizontal axis. c. Write the budget constraint and find the equation of the slope of this line (dk/dL)arrow_forwardplease only solve part d, e, farrow_forwardA firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?arrow_forward
- Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.arrow_forwardQUESTION 39 The folllowing table shows data for a simple production function. Capital (K). Labor (L) 10 0 10 1 10 2 3 4 5 6 10 10 10 10 TP or Q AP MP 6 14 20 14 8 Assume that the cost of capital, PK, is $50 per unit, and the cost of labor, PL, is $100 per unit. Marginal cost, MC, is at minimum when labor, L, is equal to O2 units. O4 units. O 3 units. 5 units.arrow_forwardQuestion 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?arrow_forward
- Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…arrow_forwardSuppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.arrow_forwardI don't believe part (b) was fully answered. Can you please solve it with more detail?arrow_forward
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