5. Selpats produces pens with the production function f(k, l) = 200vkl. The price ofcapital 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 thelong-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 totalcost function and the short-run marginal cost function. Explain the relationship betweenthe 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.

Given production function Y=200KLPrice of Capital=40Price of Labor=10

Answered: 5. Selpats produces pens with the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α
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.
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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
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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.
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 600 bottles per day (i. e. MPK = 600). An additional man-hour of labor would increase output by 1200 bottles per day (i. e. MP₁ = 1200). The price of a man-hour of labor is $40 per hour. The price of a machine-hour of fermentation capacity is $8 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 choosing 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 $20 per hour. How does this change the answer from part 1?
In order to make a replacement decision, a firm calculated the equivalent annual cost of owning an asset as follows: EUAC Annual EUAC Replacement Capital Repair Repair Period Costs Costs Costs 1 2 3 4 5 $1,287- $1,082 $400 $189 $976 $600 $298 in 1 year $812 $800 $437 $673 $1,200 $592 When should the company replace the equipment? in 2 years O in 4 years in 5 years in 3 years
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Let us consider the cost implications of the short-run production schedule from assignment number 7, where capital was fixed at 2 units of capital. Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 In this scenario, since we only have two inputs (Capital and Labor), and since the amount of capital is fixed, the cost of total cost capital would also be Total Fixed Cost (TFC) and since labor is variable, the total cost of labor would be Total Variable Cost (TVC). In that context, assume that the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is also $30 per unit of labor per period. (a) Use this information set up a diagram (using excel) that shows total cost (TC) and total variable cost (TVC) of the firm per period in the short run with the level of output on the horizontal axi
1. Given the production function: q = 2KL, (a) Fill in the table below which has information on the short-run production function, the marginal product of labor (MPL), and the average product of labor (APL) if capital is held fixed at 3 units in the short-run. Labor Quantity of Output (MPL) (APL) 0 1 4 9 16 25 (b) Plot the short-run production function. (c) Plot the marginal and average products of labor on a new graph. (d) Does the law of diminishing marginal returns apply? If so, at what level of labor do diminishing marginal returns set in? (e) What is the relationship between the marginal product of labor (MPL) and the average product of labor (APL)? (f) If the amount of capital increased to 6 units, what would happen to your graphs in part C)?
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