Please see the attached photo. Only solve part d, e, f and g Suppose in the long-rung the production function of a competitive firm is Q=f(L,K)= L2/³K¹/4, where Lis the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost ofcapital is r, which is the interest rate. The price per unit of output is p.a. Write down the profit as a function of K and L.b. Find the marginal products of K and L: MPK and MPLC. Now multiply MPK and MPL by the output price, p, to get the marginal revenues ofcapital and labor, respectively.d.e.The optimal levels of inputs satisfy the condition: marginal revenue of each input equalsits marginal cost. The marginal cost of capital is r, and the marginal cost of labor is w.Solve the resulting system of two equations for the profit-maximizing levels of inputs.What is the profit maximizing level of output?Does this production function exhibit increasing, decreasing or constant returns toscale?f. If instead of above production function, we have f(L,K)= L2/³K²/3 for a competitive firm,what will be the profit-maximizing level of the output? What are the returns to scale ofthis new production function?g. Finally, solve the profit-maximization problem for a competitive firm if the productionfunction is exhibiting constant returns to scale, and has the form f(L,K)= L2/3K¹/3. Howmany solutions does this problem have? What is the maximum profit that thecompetitive firm can earn?

Given Production function = Q=L23K14 Price per output = p Cost per unit of labor = w Cost of capital…

Suppose in the long-rung the production function of a competitive firm is Q=f(L,K)= L2/³K¹/4, where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. The price per unit of output is p.

Suppose in the long-rung the production function of a competitive firm is Q=f(L,K)= L2/³K¹/4, where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. The price per unit of output is p.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.

Question

Please see the attached photo. Only solve part d, e, f and g

Suppose in the long-rung the production function of a competitive firm is Q=f(L,K)= L2/³K¹/4, where L
is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of
capital is r, which is the interest rate. The price per unit of output is p.
a. Write down the profit as a function of K and L.
b. Find the marginal products of K and L: MPK and MPL
C. Now multiply MPK and MPL by the output price, p, to get the marginal revenues of
capital and labor, respectively.
d.
e.
The optimal levels of inputs satisfy the condition: marginal revenue of each input equals
its marginal cost. The marginal cost of capital is r, and the marginal cost of labor is w.
Solve the resulting system of two equations for the profit-maximizing levels of inputs.
What is the profit maximizing level of output?
Does this production function exhibit increasing, decreasing or constant returns to
scale?
f. If instead of above production function, we have f(L,K)= L2/³K²/3 for a competitive firm,
what will be the profit-maximizing level of the output? What are the returns to scale of
this new production function?
g. Finally, solve the profit-maximization problem for a competitive firm if the production
function is exhibiting constant returns to scale, and has the form f(L,K)= L2/3K¹/3. How
many solutions does this problem have? What is the maximum profit that the
competitive firm can earn?

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