In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q =f(L,K), q=6LK+4L² ²-(3) ₁². where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the character.)

In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q =f(L,K), q=6LK+4L² ²-(3) ₁². where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the character.)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3.4
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?
1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes
Consider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?
Q2. Given a production function Q = f (K, L) = K² + 2L, both capital and labour are doubled, does this production function display increasing, decreasing or constant returns to scale? Show the complete working and explain what returns to scale is noticed.
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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
Consider the production function: F(L, K) = L0:2K0.7. %3D The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. (a) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L, K) = (1,1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination? r (b) Compute the quantity of labour and capital that this firm would use to produce y = 2 at the minimum cost. How much would this cost be? What is the average cost and the marginal cost for that production level? Hint: for this part, you can use directly (without providing the derivation) any results derived in the lecture or tutorials. (c) Derive the equation of the isoquant for y = 2 (with K in the…
suppose Mark operates the production of lawnmowers at Mark Mowers and Bros. Using inputs like labor (L) and capital (K). over his time as a production manager, he has found out that the production function, in the long run, is Q=500*min (L,7K). Given this information, help him determine the following. b. Assume for the time being that he has only one unit of capital to employ in this factory. What would be the total product, the marginal product, and the average product of the labor curve? Draw all three of them. Also make sure that you create a table using the different combinations of L and K that helps you in determining the shape of these curves.
QUESTION 8 Consider the production function F(A,K) = A*In(K), where A = 3 is a constant. What is the marginal product of capital equal to when K = 2? (State your answer to 2 decimal places.)
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When labor is doubled and capital is tripled, a firm's output increases 2.5 times. Which of the following is true? We need more information to determine the degree of returns to scale of this firm's production function. This firm's production function must exhibit increasing returns to scale. This firm's production function must exhibit decreasing returns to scale. This firm's production function must exhibit constant returns to scale.