Answered: Consider a perfectly competitive firm…

Consider a perfectly competitive firm with the following production function: q=L025K0.25 a. Solve for the long run profit maximizing labor demand and capital demand functions.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.3P

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Question

Solve a

Consider a perfectly competitive firm with the following production
function: q=L025K0.25
a. Solve for the long run profit maximizing labor demand and capital demand
functions.
b. What is the profit maximizing long run firm supply function?

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Solve b
A5
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Assume a firm has the following short-run production function: q (L) = L + 2L² – 1³ Given the production function above, answer the following two questions: A) If this firm is going to maximize profits in the short-run by producing a strictly positive level of output (q> 0), what is the lowest level of labor (L) they would employ? Minimum level of labor = 3 B) Now suppose the firm must pay each unit a labor (L) a wage of $6 (w = 6). If this firm is maximizing their profits in the short-run by hiring 4 units of labor (L that they can charge for each unit of output they produce? Price = dollars - 4), what must be the price (p)
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True or false and explain Suppose a firm’s marginal product of labour is MPL = 10/L, where L is measured in labour hours, the price of the product is $600, and the cost per hour of labour is $30. The firm currently employs 150 labour hours. In order to maximize the firm’s profits in the short run, the manager should increase its labour employment by 40 labour hours.
Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
Please answer fast
Answer the attached question
Consider the following short-run production function (where L – labour, Q - output): Q = 10L - 0.5L^2Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input as it needs at $20 per unit.Determine the marginal value of product with respect to labour.Determine the marginal cost of labour (factor cost function).Determine the optimal value of L, given that the objective is to maximize profits.
B. Consider a firm who sells output at p=10 and has a short run production function Q(L)=20L-L2. Its wage rate function is w=40+2.5L. How much wage will it pay?