Question: A paint manufacturing company has a production function Q = 2K + 2L^1/2 . a. Use the Lagrangian method to derive the input demand functions

A paint manufacturing company has a production function Q = 2K + 2L^1/2 .

a. Use the Lagrangian method to derive the input demand functions for L and K for an interior optimum.

b. What is the cost-minimizing input combination to produce 100 units of output if the firm faces input prices w= 1 and r =50? Draw an isoquant-isocost diagram and show your cost-minimizing bundle. c. Verify that the firm's cost-minimizing input combination to produce Q = 100 involves no use of capital when r = 110 keeping w = $1. What is the amount of labor the firm would use in this situation? d. In part ( c ), is MRTS equal to the input price ratio? If not, does it make sense that the equality is not satisfied at the optimal bundle?

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!

I. Which of the following is correct? a) The pivot of the budget line shows the substitution effect while a slope gives the income effect. b) The pivot of the budget line shows the substitution...

Kindly help me solve these Problem 2 (30 pts) Explain your answers! A firm has a production technology involving two inputs, capital (K) and labor (L). /(K; L) - K1/3LV/3. The price of capital is r;...

Economics questions... . Suppose that a market is composed of two firms that simultaneously choose quantities. Firm 1 has 22 a cost function C1(q1) = q1^2. Firm 2 has a cost function C2(q2) =...

1. The Zimmerman Company digs ditches. It faces the production function, Q = LlK, where Q is the number of ditches dug, L is hours of labor, and K is the number of digging tools. (a) Would we...

tax Consider the market for apple juice. In this market, the supply curve is given by QS = 10PJ 5PA and the demand curve is given by QD = 100 15PJ + 10PT , where J denotes apple juice, A denotes...

answer allk A firm produces output using the technology y = 1 1,000 KL1 2 , where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and y denotes the yearly output. The...

these are 2 questions i need help. please help me asap thanks Acrobat Reader File Edit View Window Help K * 67% A Wed 8 Apr 14:30 Q DE ... ECON1056 Take-home Exam.pdf Home Tools ECON1056 Take-... X...

3. (15 points)(Competitive Firm) Suppose a competitive firm has the production function of f(x1, X2) = X] T2 . The output and input markets are competitive, and their prices are denoted by p, w1, and...

1. (27 points) For each of the following production functions, sketch a representative isoquant (2 points). Calculate the marginal product for each input, and indicate whether each marginal product...

Consider the following production function for three firms operating in the same industry using capital ( K ) and labor ( L ) as inputs. Firm E Q = K ^ 0 . 7 L ^ 0 . 3 Firm F Q = K L ^ 2 For each...

Describe the concept of HRD (Human Resource Development) change in an organization. In addition, rationalize suitable interventions to address emotions of change by choosing the theory of...

Assume that an auditor is reviewing a file containing twenty-five fields of data, only five of which are relevant to the auditors objective. Explain how ACL can help in this situation.

A bond with a $ 1 0 0 annual interest payment, $ 1 0 0 0 face value, and five years to maturity ( not expected to default ) would sell for a premium if interest rates were below 9 percent and would...

Suppose that a car mechanic offers you a deal that for the next 3 years any breakdowns will be covered, so long as you bring your car in for $54 preventative maintenance sessions each month. If you...

2. Start with a person you want to model. a. Use the five positions to investigate how this person positions himself in relation to others, i.e. how he uses the five positions in his interaction with...

1. Start with a leader that you want to model. a. What is the stated purpose of this person? b. What is the vision of this person? c. How does he seek to achieve his purpose and vision? d. What does...

2. Now change the performance so that you play out the dream in your inner the-atre. Apply colours to the images you envision. Give some pictures a stronger colour than others and vice versa. Also...