Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

Question

Question

Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

a. Find marginal product of labor and marginal product of capital.

b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.

c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.

business economics

Add a comment Improve this question Transcribed image text

Answer 1

✔ Recommended Answer

Answer #1

Ans 5.) (a)

Marginal product_Labor = d(Q)/d(L)

= 8K + (1/(L)^1/2)

Marginal product_{capital =} 8L

(b) Marginal rate of technical substitution is the amount of one input that need to be given up in order to hire an extra unit of other input.

MRTS_Lk = MPL / MP_K

MRTS = (8K + (1/(L)^1/2)/(8L)

MRTS = K/L + (1/8L^1/2)

(C)

Q = 8(10)(16) + v/16

Q = 1280 + 4 = 1284 units

Add a comment

Answer 2

Similar Homework Help Questions

Suppose the production function for automobiles is ? = ?? where Q is the quantity of...

Suppose the production function for automobiles is ? = ?? where Q is the quantity of automobiles produced per year, L is the quantity of labor (man-hours) and K is the quantity of capital (machine hours). a) What is the total product (number of automobiles) if the firm uses 25 man hours and 2 machine hours? b) Sketch the isoquant corresponding to a quantity of Q=50. c) What is the general equation for the isoquant corresponding to any level of...
Consider the following Cobb-Douglas production function, where α Find the equation for the isoquant when Q...

Consider the following Cobb-Douglas production function, where α Find the equation for the isoquant when Q 4,000. K-(Properly format your expression using the fools in the paiette. Hover over tools to see keyboard shortcuts Eg, a fraction can be created with the /character) The marginal rate of technical substitution (MRTS) when Q 4,000 and L-50 (with capital measured on the vertical axis and labor measured on the horizontal axis) is MRTS (Enter a numenic response using an integer)
Let q = L½k½ denote the production function for a firm making long-run decisions

Let q = L½k½ denote the production function for a firm making long-run decisions, that is K (capital) and L (labor) are now variable. a. Place k on the Y-axis and L on the X-axis and illustrate an isoquant when q=100.b. Derive an expression for the MRTS (the marginal rate of technical substitution) for any level of q.

Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant...

Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant when Q=4,000 16.000.000 (Property format your expression using the tools in the palette. Hover over fools to see keyboard shortcuts. Eg, a fraction can be created with the character.) The marginal rate of technical substitution (MRTS) when Q ) 4,000 and L - 100 (with capital measured on the vertical axis and labor measured on the horizontal 2 MRTS - (Enter a numeric response...
Suppose a firm has a production function given by Q=2K+L, where L is labor, K is...

Suppose a firm has a production function given by Q=2K+L, where L is labor, K is capital and Q is the quantity of output. Which of the following statements is WRONG? A. The firm is exhibiting constant returns to scale B. The firm’s marginal product of capital is constant C. The firm’s marginal product of labor is constant D. The firm’s marginal rate of technical substitution depends on the amount of inputs
You are given the following production function Q = K1/3L2/3, where Q is output, L is...

You are given the following production function Q = K1/3L2/3, where Q is output, L is labor, and K is capital. First, calculate the marginal product of capital and the marginal product of labor. Next, calculate the marginal rate of technical substitution of labor for capital, MRTSL,K. What does this tell you about the production function?

Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor...

Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor input. Let K>0, L>0. 1. What are the marginal products of capital and labor re- spectively? 2. Please compute the technical rate of substitution (we as- sume K is on the horizontal axis). 3. Dose this production function show diminishing technical rate of substitution (in absolute value) when K increases? Please give a brief proof. 4. Please prove that this production function features increas-...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...

Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2 a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function. b) What is the firm’s marginal cost? c) For this problem, you will sketch the graph of the firm’s isoquant for Q...

2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...

2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?

Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

Homework Answers

Add Answer to:
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

Post as a guest

Earn Coins

Suppose the production function for automobiles is ? = ?? where Q is the quantity of...

Consider the following Cobb-Douglas production function, where α Find the equation for the isoquant when Q...

Let q = L½k½ denote the production function for a firm making long-run decisions

Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant...

Suppose a firm has a production function given by Q=2K+L, where L is labor, K is...

You are given the following production function Q = K1/3L2/3, where Q is output, L is...

Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor...

Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...

2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...

Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

Homework Answers

Add Answer to: Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

Post as a guest

Earn Coins

Add Answer to:
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.