The Whoville Marble Collective (WMC) makes fancy marbles for picky Whos. WMC's output is given by Q = 20K0.75 0.25, where Q is WMC's annual output (measured in 1000s of marbles), K is their annual capital input and L is their annual labor input. WMC's capital input costs PK = $8000 per unit and their labor input costs p₁ = $25000 per unit. Assuming that WMC's annual production budget is B = $800,000, their maximum annual output is ... 412,891 marbles. 726,085 marbles. 578,634 marbles. O...=857,232 marbles.

The Whoville Marble Collective (WMC) makes fancy marbles for picky Whos. WMC's output is given by Q = 20K0.75 0.25, where Q is WMC's annual output (measured in 1000s of marbles), K is their annual capital input and L is their annual labor input. WMC's capital input costs PK = $8000 per unit and their labor input costs p₁ = $25000 per unit. Assuming that WMC's annual production budget is B = $800,000, their maximum annual output is ... 412,891 marbles. 726,085 marbles. 578,634 marbles. O...=857,232 marbles.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Assume there is a linear isoquant where the input combination K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100? $20 $10 $50 $100
Assume there is a linear isoquant where the input combination K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?
Please answer in detail according to the picture. Show that the cost function is homogeneous of degree 1/(α+β) in output. How do the returns to scale (degree of homogeneity of the production function) relate to the propertiesof the cost function? Does this make sense to you? Explain clearly why.
c) The product function of a company is given by 1 v2 , where v is the number of units of fv) = the input factor. The company buys the input factor at a fixed price per unit given at 5 q =. Assume further that the company has fixed costs which in their entirety are sunk costs, and which is given by F= 100 . Show that the company's cost function is CO 20= y? +100 . d) Take as a starting point the information given in task (c), and assume that the company can sell finished goods in the market at a fixed price given by = 800 Formulate the company's profit function, and calculate which production volume maximizes corporate profits.
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Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3) The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.
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Could you solve d,e,f ? Thank you
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The short run production function of a competitive firm is given The short-run production function of a competitive firm is given by f (L) = 6L2/3, where L is the amount of labor it uses. (For those who do not know calculus—if total output is aLb, where a and b are constants, and where L is the amount of some factor of production, then the marginal product of L is given by the formula abLb−1.) The cost per unit of labor is w = 6 and the price per unit of output is p = 3. (a) Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). What is the slope of each of the isoprofit lines? (b) How many units of labor will the firm hire? (c) Suppose that the wage of labor falls to 4, and the price of output…
Consider the following production functions, to be used in this week’s assignment:(A) F(L, K) = 20L^2 + 20K^2(B) F(L, K) = [L^1/2 + K^1/2]^2 (i) Neatly draw the Q = 2,000 isoquant for a firm with production function (A) given above,putting L on the horizontal axis and K on the vertical axis. As part of your answer, calculate three inputbundles on this isoquant. (ii) Neatly draw the Q = 10 isoquant for a firm with production function (B) givenabove. As part of your answer, calculate three input bundles on this isoquant. For your three input bundles,choose one with L = 0, choose one with K = 0, and the third with L = K. PLEASE SHOW ALL WORK