Question

Suppose that the production function has the form ?=?∙√?+? where y is output, A is a...

Suppose that the production function has the form ?=?∙√?+? where y is output, A is a positive constant, ? is labor input, and B is another constant which may be positive, negative or zero.

a) Graph the level of output, ?, versus the quantity of labor input, ?.
b) Is the marginal product of labor positive? Is it diminishing in ??
c) Describe the wealth and substitution effects from an increase in the coefficient ?.
d) Describe the wealth and substitution effects from an increase in the coefficient ?.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
production function Consider a firm that produces a single output good Y with two input goods:...
production function Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R 2 + → R+ defined by f(l, k) = √ l + √ k, where l is the quantity of labor and k is the quantity of capital. (a) In an appropriate diagram, illustrate the map of isoquants for the firm’s production function. (b) Does the...
Suppose that a rm has a production function given by Q= 5L^2/5K^1/5 (a) Show that there...
Suppose that a rm has a production function given by Q= 5L^2/5K^1/5 (a) Show that there is a positive and diminishing marginal product of labour, and a positive and diminishing marginal production of capital. (b) Show that increasing K leads to an increase in the marginal product of labor, and increasing L leads to an increase in the marginal product of capital.
A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L...
A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L denote quantities of capital and labor, respectively. Derive expressions (formulas) for the marginal product of each input. Does more of each input increase output? Does each input exhibit diminishing marginal returns? Prove. Derive an expression for the marginal rate of technical substitution (MRTS) of labor for capital. Suppose the price of capital, r = 1, and the price of labor, w = 1.   The...
Suppose the production function for a bakery is: Q = 4K0.4L0.6 where Q is the number...
Suppose the production function for a bakery is: Q = 4K0.4L0.6 where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. Use calculus for the following: a. determine a function for the marginal product of labor. b. determine a function for the marginal product of capital. c. find the marginal rate of technical substitution. d. discuss how MRTSLK changes as the firm uses more...
Consider the following production function Y=z*(a*K + (1-a)*N) where z represents total factor productivity, a is...
Consider the following production function Y=z*(a*K + (1-a)*N) where z represents total factor productivity, a is a parameter between 0 and 1, K is the level of capital, and N is labor. We want to check if this function satisfies our basic assumptions about production functions. 1. Does this production function exhibit constant returns to scale? Ex- plain 2. Is the marginal product of labor always positive? Explain 3. Does this function exhibit diminishing marginal product of labor? Ex- plain...
Suppose the economyís production function is Y = K0:3L0:7 Show the the production function slopes upward...
Suppose the economyís production function is Y = K0:3L0:7 Show the the production function slopes upward from left to right. Show that the production function features diminishing marginal product of labor. When constant return to scale is assumed, derive the per worker produc- tion function. .
Suppose the economyís production function is Y = K0:3L0:7 Show the the production function slopes upward...
Suppose the economyís production function is Y = K0:3L0:7 Show the the production function slopes upward from left to right. Show that the production function features diminishing marginal product of labor. When constant return to scale is assumed, derive the per worker produc- tion function. .
4. output Q according to the production function Q = 6K1/3L1/2, where K = capital and...
4. output Q according to the production function Q = 6K1/3L1/2, where K = capital and L =labor. A. Calculate the marginal product of capital. Calculate the marginal product of labor. Calculate the marginal rate of technical substitution A technological advance occurs which changes the production function to Q = 2KL. D. Calculate the new marginal product of capital. E. Calculate the new marginal product of labor. F. Calculate the new marginal rate of technical substitution for Lazy J Enterprises....
A firm’s production function is ? = ?Lα ?β where A, α, and β are positive...
A firm’s production function is ? = ?Lα ?β where A, α, and β are positive constants. The firm currently uses 500 units of labor and 40 units of capital. If the firm adds 1 more unit of labor, what happens to productivity of capital? Explain. b. Given a production function Q = f(L, K), if marginal product of labor and marginal product of capital are both positive, then this function displays diminishing MRTS. Explain if this statement is true...
Consider a production function Y=zF(K,Nd) Which of the following properties we assume for F? 1. Constant...
Consider a production function Y=zF(K,Nd) Which of the following properties we assume for F? 1. Constant returns to scale. 2. Output increases with increases in either the labor input or the capital input 3. The marginal product of labor decreases as the labor input increases. 4. The marginal product of capital decreases as the capital input increases. 5. The marginal product of labor increases as the quantity of the capital input increases. A) 1,2,3,4 and 5 B) 1,2,3 and 4...