The production function of a firm is as follows: y(K,L) = 500 1 -KLOS, where Kis capital measured in machine-hours, L is labor in person-hours, and y is the yearly output. The hourly wage rate, w, is Ł10, and the hourly rental rate of capital, r, is £20. a. Show what type of returns to scale the technology of this firm displays (constant, increasing, or decreasing). b. Calculate the marginal products of labor and capital. c. Derive the firm's short-run cost function (as a function of output given the factor prices) if the capital is fixed at 10,000 machine hours. Start with setting the short-run cost minimization problem of the firm subject to the technology constraint. d. Derive the firm's short-run marginal cost function and the short-run average cost function. At what level of output do these curves intersect? Show that at this point, the average cost function is at its minimum.

The production function of a firm is as follows: y(K,L) = 500 1 -KLOS, where Kis capital measured in machine-hours, L is labor in person-hours, and y is the yearly output. The hourly wage rate, w, is Ł10, and the hourly rental rate of capital, r, is £20. a. Show what type of returns to scale the technology of this firm displays (constant, increasing, or decreasing). b. Calculate the marginal products of labor and capital. c. Derive the firm's short-run cost function (as a function of output given the factor prices) if the capital is fixed at 10,000 machine hours. Start with setting the short-run cost minimization problem of the firm subject to the technology constraint. d. Derive the firm's short-run marginal cost function and the short-run average cost function. At what level of output do these curves intersect? Show that at this point, the average cost function is at its minimum.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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V1
The production function for a firm is ?=−0.6?^3+18?^2 ?+10Lwhere q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. ???=−1.8?^2+36?+10 b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram.
can you explain the solution for part b like for example how did they get M=y^2/2 and L=2y^2
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Is each of the following statements true or false? In either case, briefly justify your answer. (a) If a firm has economies of scale, then its average cost is decreasing and lower than its marginal cost. (b) A firm whose total cost function is C(Q)=Q^2+Q must have economies of scale. (c) A firm with total cost function ?(Q) = 3Q+2 must have constant returns to scale. Plz do fast asap
What is the distinction between the laws and of returns and the returns to scale?
Give relation between average product and marginal product.
If a business is experiecing diminishing marginal product of labor then A. its fixed costs must be increasing B. its total cots must be decreasing C. its marginal costs must be increasing D. its implict costs must be decreasing (please explain each choice)
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Which of the following diagrams shows isoquants for a Cobb-Douglas production function? A X1 B X2 X1 X1 D X2 X1 O A OB OC OD
Production Point Capital (K) Labor (L) Output (Q) A 1 1 2 B 2 2 C 1 3 D 2 4 E 1 5 F 2 6 G 1 7 H 2 8 X The profuction function is given as: Q=αK + βL B andf E lie on the same isoquant, while D and G are on a higher isoquant. 1. a. Determine the production function and solve for the value of X? b.The given production function shows a long-run production. Explain the reason behind this. c. Keeping capital fixed at 2 unitsk, what is the marginal product of the 10th unit of labor?