3. Answer all parts (a)-(e) of this question.Consider the following production function: Q = 3K&L, with marginal products given byL3MPL = Kand MPKDefine the unit prices of L and K as w and r, respectively.Finally, assume that the firm takes the price of its product, p, as given and maximizes profits.L3K3(a)Imagine capital is fixed at Ko = 1 in the short run. What is the short-run costfunction of the firm? Explain briefly.(b)(c)(d)(e)when rw = 1?What is the long-run cost function of the firm?What is the long-run supply function of the firm?What is the profit function of the firm?Now suppose that set-up costs are £1. What is the shut down rule of the firm

MPL(Marginal product of labor) is the extra/additional output that the firm receives from employing…

3. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K3 L3, with marginal products given by MPL = Ka and MPK = Define the unit prices of L and K as w and r, respectively. Kś Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? (b) (c) (d) Now suppose that set-up costs are £1. What is the shut down rule of the firm (e) when r = w = 1?

3. Answer all parts (a)-(e) of this question. Consider the following production function: Q = 3K3 L3, with marginal products given by MPL = Ka and MPK = Define the unit prices of L and K as w and r, respectively. Kś Finally, assume that the firm takes the price of its product, p, as given and maximizes profits. L3 (a) Imagine capital is fixed at Ko = 1 in the short run. What is the short-run cost function of the firm? Explain briefly. What is the long-run cost function of the firm? What is the long-run supply function of the firm? What is the profit function of the firm? (b) (c) (d) Now suppose that set-up costs are £1. What is the shut down rule of the firm (e) when r = w = 1?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Please no written by hand The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in order to produce fish. Currently, the company has no fixed inputs and pays $12 per hour for labour (w) and $16 per hour for capital (r). The quantity of fish produced per day (Q) is 153. A. Derive the conditional input demand functions for labour (L) and capital (K) for IFC. B. What is cost-minimizing amount of labour and capital that IFC should hire and rent? C. Determine the minimum cost of producing 153 units of output? D. Use the isocost and isoquant to illustrate the optimal choice of this firm.
Please solve Figure 1 below. Figure 1 (a) What assumption does Figure 1 make about the nature of the production function of a firm and what does point A represent? Explain your answer. (b) Reproduce Figure 1 provided in the question. By making appropriate inferences from it, work further to show a new isocost line for the cost level of $1000 on the same figure, if wages fall by 10% while the rental rate on capital increases by 20%. Explain your work carefully. (c) What input combination will the firm use to produce output level of 100, if wages fall by 10% while the rental rate on capital increases by 20%? Explain your answer.
Which of the following statements is (are) TRUE?I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output. IIII, II, and IIIII and II Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Problem 3 Suppose a firm's technology is described by the production function f (C,k)=2ek. Hence, the M PL = 2k and the MPK 26. Suppose also the firm operates in a perfectly competitive environment and that the price of capital is r-$1 and the price of labour is w$1. Consider the situation described in Problem 3. Does the firm's technology exhibit increasing. decreasing or constant returns to scale? O Increasing returns to scale O Decreasing returns to scale O Constant returns to scale Question 32 Consider the situation described in Problem 3. What is the long-run cost of producing 50 units of output for this firm?
2. Which of the following production functions with inputs K, L, and H exhibits Constant Returns to Scale (CRS)? (Assume Ā > 0 is a constant) a) Y = AK/2L/2 b) Y = ĀK/2L/3H/4 c) Y = ĀK/2 – L/H d) Y = ĀKL/2H\/2
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
6
A firm is able to adjust both L and K and has a production function q = KL, where K is the amount of capital and L is the amount of labor it uses as inputs. The cost per unit of capital is r and the cost per unit of labor is w. The (conditional) demand for capital (also known as the optimal level of capital) is given by: O qwr O the square root of qr/w O qw/r O q/wr O the square root of qw/r
2. A firm faces the production function 1 Q = f(K,L) = 80 [0, 4K-0,25 +0,4L-0,25] 0.25. It can buy the inputs K and L at prices per unit of 5 TL and 2 TL respectively. What combination of L and K should be used to maximize output if its input budget is constrained to 150 TL?
Suppose the production function is given by f(K,L) = 3Kl, where K denotes capital and L denotes labor. The price of capital is 2 TL/machine-hr, the price of labor is 24 TL/person-hr, and capital is fixed at 4 machine-hr in the short run. a) Find the short-run TC, TVC, and TFC curves for this production process. Sketch them on a single graph. Do not forget to label all axes and necessary points on your graph. b) Find short-run ATC, AVC, AFC, and MC curves for this production process. Sketch them on a single figure. Do not forget to label all axes and necessary points on your graph.
can you show me steps to solve this
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.