Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...

Question

Question

Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...

Given the following production function, show the results in the LaGrange method or Marginal rate of substitution.

wPij9HatvsVOwAAAABJRU5ErkJggg==

Given that your budget is limited to 100, and the price of x = 5 and y = 10. Find the following.

a) How much of x and y will be produced?

b) What is the technical rate of substitution? If x represents humans and y machines, which of them will be working more?

business economics

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Anty x0.3 y2 Psocast line tend apet Line 100= 5x + 10y dn 20 X+2Y Lagron gian marimizahan sngs (20-1-27) r0.3 112 -0.7 0.3X -

Add a comment

Answer 2

Similar Homework Help Questions

2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a....

2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a. For some w, y, use the Lagrangean method to derive demand functions by finding the cost-minimizing combinations of k and I in terms of q, w, and y (so the cost function is the objective function, and the production function is the constraint). (10 points) b. What is the rate of technical substitution (RTS) for this function? (5 points) C. Presume that the firm...
You might think that when a production function has a diminishing marginal rate of technical substitution...

You might think that when a production function has a diminishing marginal rate of technical substitution of labor for capital, it cannot have increasing marginal products of capital and labor. Show that this is not true, using the production function Q = L2K2.
4. Consider the production functions given below: a. Suppose that the production function faced by a...

4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...

6. Suppose the production function takes on the following form: a) What is the marginal rate...

6. Suppose the production function takes on the following form: a) What is the marginal rate of technical substitution? Evaluate it at L5 and K 7. (5 points) b) What are the returns to scale for this production technology? (5 Points)
3. Given a utility function U(x, y) -rys, (a) Show that the marginal rate of substitution,...

3. Given a utility function U(x, y) -rys, (a) Show that the marginal rate of substitution, MRS (b) For commodity bundles for which y how does the MRS depend on the values of α and β? Develop an intuitive explanation of why, if α > β, MRS > 1.
An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten...

An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten dollars (I = $10) The price of item x is $1. The price of item y is $1. Maximize this consumer’s utility subject to a budget constraint using the Lagrange Multiplier method. At what point does the marginal rate of substitution equal the price ratio?

Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1) consider, α = 0.2 and σ = 0.7. The first factor is...

Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1) consider, α = 0.2 and σ = 0.7. The first factor is currently used in the amount x1 = 9, and the second factor is used in the amount x2 = 3. a) When (x1,x2) = (9,3), how much output is being produced? Output: b) When (x1,x2) = (9,3), what is the marginal product of factor 1? Marginal product: c) When (x1,x2) = (9,3), what is the average product of factor 1? Average product: d) When...
3. Consider the following production function with two inputs X1 and x2. y = alnx +...

3. Consider the following production function with two inputs X1 and x2. y = alnx + Blny a. Derive the equation for an isoquant (assuming x is on the y-axis). b. Derive the marginal product of input x. c. Derive the marginal product of input x. d. Derive the marginal rate pf technical substitution (MRTS).
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution.

For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) $Q=L+K$(b) $Q=2 L^{2}+K^{2}$(c) $Q=L^{1 / 2} K^{1 / 2}$

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?

Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...

Homework Answers

Add Answer to:
Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...

Post as a guest

Earn Coins

2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a....

You might think that when a production function has a diminishing marginal rate of technical substitution...

4. Consider the production functions given below: a. Suppose that the production function faced by a...

6. Suppose the production function takes on the following form: a) What is the marginal rate...

3. Given a utility function U(x, y) -rys, (a) Show that the marginal rate of substitution,...

An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten...

Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1) consider, α = 0.2 and σ = 0.7. The first factor is...

3. Consider the following production function with two inputs X1 and x2. y = alnx +...

For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution.

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

Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...

Homework Answers

Add Answer to: Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...

Post as a guest

Earn Coins

Add Answer to:
Given the following production function, show the results in the LaGrange method or Marginal rate of substitution. Give...