Consider the following Cobb-Douglas production function: Y = 10L04K04. Suppose that theprice of labor is w = 20 and the price of capital if r = 40.a- Derive the total cost curve for this production function.b- Derive the marginal cost curve for this production function.c- Plot the marginal and total cost curves for q = 1,2,3,4,5. What does it tell you abouteconomies of scale for the production function?d- Suppose that the wage rate went up from 20 to 30. What would happen to the totalwage bill relative to total costs,wL;? What would happen to total costs?wL+rk*

Answered: Image /qna-images/answer/958f2e78-bdfd-4671-aebc-9ca8478af493.jpg

Answered: Consider the following Cobb-Douglas…

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, a firm cannot vary its capital and operates with K = 9. It can, however, vary the amount of labor (L) that it uses. For each production function below, explain why the firm will or will not experience diminishing marginal returns to labor in the short run. a) q= 35L +40K b) q= L^0.5 K^0.5
The production function of producing an item is given by 3K Q = 744 VR - where K is the capital required. Calculate the marginal product of capital if the current capital is 512.
The equation below is a production function, Q = (200)L + (100)K – (0.2)L2 – (0.1)K2 , where Q is output, L is labor and K is capital. What is the Marginal Product of Labor and capital of this function?
The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output?
Consider the production function q=√L+8K^(3). Starting from the input combination (3,6), does the production function exhibit increasing, constant or decreasing returns to scale if inputs double?
Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True False
Suppose that a firm's production function is: a = 3L * K ^ 0.5 The cost of capital is $30/unit; the cost of labor is $20/unit. What is the minimum cost of producing q = 243 ?
Explain the relationship between the production function and the average costs and marginal costs curve of a firm.
A farm producing wheat has the following production function Q = 4L + 3K. Does the above function exhibit increasing, constant, or decreasing returns to scale? Prove and explain your answer.
A firm's production function is given by Q = 20L0.8 K0.2. At that moment, the firm sets = 1,000 and K = 1,000. Which of the following combinations of L and Klies on the same isoquant? L = 1,063.9; K = 698.7 L= 1,063.9; K = 698.7 L=698.7; K = 1,063.9 L = 1,302.3; K = 936.1 L 936.1; K 1,302.3
Looking at the following plot of a firm's production function, represented by isoquants for production levels and isocost lines for different total costs of production. Which of the following are true? 101 00 9 K, Capital per unit time Cost $38.80 2 Cost $18:40 6 L. Labour per unit time 10 Y Y 4 Y 2 a. Points a and b are each cost minimizing points for the firm at different levels of output. b. Point d will have higher output and lower total cost than point c c. Point e has less output than point b, but a higher total cost. d. The production function exhibits increasing returns to scale. e. It's clear that Point c does not correspond to a cost-minimizing bundle of inputs.

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