1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L% where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. -(주)" For this production, MP, = and MP, = 3 The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost

1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L% where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. -(주)" For this production, MP, = and MP, = 3 The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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), where q is output, L is workers, and K is the fixed number of units of capital. A specific equation for the production function is given by: or, when K = 20, q 8KL+ 5L² = q = (8×20×L) + 5L² The level of output q for 10 units of labor input is (enter your response rounded up to two decimal places). The average productivity of these 6 units of labor is (enter your response rounded up to two decimal places). The marginal productivity of using one more unit of labor input is (enter your response rounded up to two decimal places). Given the relationship between the average productivity and the marginal productivity, the average productivity of labor is 3
I am having trouble finding out the formulas to complete this question: The production function for a firm is q = -0.6L3 + 18L2K + 10L where q is the amount of output, L is the number of labor hours per week, and K the amount of capital. The wage is $100 and the rental rate is $800 per timeperiod. 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. 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. You will not be able to solve the total product curve for L as a function of output. So, instead construct a table. Headings: L q(L) APL MPL VC TC AVC AC MC w/APL w/MPL
a. A firm's long-run total cost can be written as LTC = 3000Q - 50Q2 + (1/3)Q3 and its long-run marginal cost by LMC = 3000 - 100Q + Q2. Find the range over which the firm will experience economies of scale. Explain your answer. b. A firm has a production function of Q = K * L + L, where the marginal product of labor is MPL = K + 1 and the marginal product of capital is MPK = L. The wage rate (W) is $100 per worker and the rental price (R) is $100 per unit of capital. In the short-run, capital (K) is fixed at 4. Find the minimum total cost of production in the short- and long-run if the firm produces 100 units of output.
I need this in words Not handwritten or no pic
F(L, K) = LK^3 and F(L,K) = L+3K for each of these production functions: a) draw the corresponding graph b) calculate the marginal product of labor and capital c) discuss if each marginal product is diminishing, constant or increasing d) calculate the marginal rate of technical substitution e) calculate if the function exhibits constant, increasing, or diminishing returns to scale
1/3 1/3 Bridget's Widgets produces widgets with the production function, y = x1 x2, where 1 is the quantity of labor input, x2 is the quantity of capital input, and y is the quantity of output. The per-unit price of labor input is w₁ = 20 and the per-unit price of capital input is w₂ = 80. What is Bridget's long run total cost function, C(y), given that both inputs can be varied in the long run? C(y) 20/2 C(y)-80y/ C(y)-80y = ⚫ C(y)=20y³
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1. Assume a daily production function for a firm is Q= min(3L, 4K) a, If L = 100 and K = 100 what quantity is produced? Explain why. b. What would be the cost-minimizing labor and capital combination for this firm to produce Q = 1200? (show your work) Labor = Capital = At this level of production from part b (Q-1200), if the wage rate is: w- $30 and the rental rate of capital is: r= $100, what is the total cost of production? (show your calculations) C.
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.
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.
The following equations represent the long-run production functions for four different technologies, where capital and labor are both variable inputs. For each function, indicate whether it exhibits increasing, decreasing, or constant returns to scale. Clearly show your derivations. (Note that in parts a and c, the exponents are decimals.) f(L,K)= 8L²K4 b. f(L,K)= L+7K c. f(L,K)= L³K d. f(L,K)= 4L+K? а. с.