Question: Suppose that the production function is given as a function of two inputs, L and K, where L is the quantity of labor and K

Suppose that the production function is given as a function of two inputs, L and K, where L is the quantity of labor and K is the quantity of capital, and expressed as below:

Q=32L-2L2 + 65K-4K2

The price of output is $30 per unit, the price of labor is $95 per unit, and the price of capital is $120 per unit (note, P = 30, w = 95 and r = 120).Answer the followings.

a.Derive the equations for MPL and MPK.

b.Derive the equations for the labor demand function and the capital demand function.

c.Compute the profit maximization level of employment for labor and capital.

d.What is the quantity of output at the profit maximization?

e.Compute the profit.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Economics Questions!

Suppose that the production function is given as a function of two inputs, Land K, where L is the quantity of labor and K is the quantity of capital, and expressed as below: Q=65L-4L- + 32K-2K2 The...

1. How much labor and capital should the firm hire if it wants to produce 48 units of output while minimizing its cost of production?2. How much labor and capital should the firm hire if it wants to...

Suppose a Cobb - Douglas Production function is given by the following: P ( L , K ) = 9 0 L 0 . 9 K 0 . 1 where L is units of labor, K is units of capital, and P ( L , K ) is total units that can be...

Suppose a Cobb - Douglas Production function is given by the following: P ( L , K ) = 6 0 L 0 . 7 5 K 0 . 2 5 where L is units of labor, K is units of capital, and P ( L , K ) is total units that can...

1. (a) The inverse demand function and total cost function of a designer handbag manufacturer are given as follows: P = 2000 - 100 TC = 5000 + 500Q i. Find the manufacturer's total revenue function...

Answer all.... Part III. Solow Model of Growth Suppose that the production function is given by Y=0.5 VK VN. Assume that the size of the population, the participation rate, and the unemployment rate...

The ACME Sock Company's (ASC) production function is given by Q = 30K0.4-0.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of...

The firm's short-run production function is given by Q left parenthesis K comma L right parenthesis equals space K to the power of 1 divided by 2 end exponent L to the power of 1 divided by 2 end...

Q#1 (40 marks) Suppose the firm's production function is given as Q = 10KL , where L is labor, K is capital. 1) Calculate the elasticity of substitution of this production function. (5marks ) 2) What...

Y = 1 Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.

a)The president believes that a $ 16 000 increase in the monthly advertising budget combined with an intensified effort by the sales staff, will result in an $80 000 increases in monthly sales. If...

Required: Using the information in the tables above, please calculate the expected return for this security using a two - factor model ( Industrial production and inflation ) .

Describe Municipal bonds, how are they used by government and municipalities, also how do they work for clients accounts. Please do some quick research and find some current municipal bonds, please...

=+ e. Using your graph, show the impact of an increase in u. (Hint: This change affects both curves.) Describe both the immediate and the steady-state effects.

=+ 7. Choose two countries that interest youone rich and one poor. What is the income per person in each country? Find some data on country characteristics that might help explain the difference in...

=+difference? In your judgment, how useful is the Solow model as an analytic tool for understanding the difference between the two countries you chose?