A firm’s production function is ? = ?Lα ?β where A, α, and β are positive...

A firm’s production function is ? = ?L^α ?^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.

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 or false.

1. You are trying to maximize your output subject to a budget. At one possible input bundle, where the constraint is binding, you find MPL > MPK. As long as MPL > MPK, you should keep spending more of your budget on labor and less on capital. Briefly explain if this statement is true or false
1. A factory has production function Q = f(L, K).

In year 1: 212 = f(78, 144)

In year 5: 309 = f(117, 216)

What kind of returns to scale does the production function display over the five years period? Explain.

If a firm’s fixed cost decreases. The firm’s should take advantage of this drop by producing more. Briefly explain if this statement is true or false

Expert Solution

Rahul Sunny answered 2 years ago

A = [(α −β −β), (−β α −β), (−β −β α) ] (each row is in...

A = [(α −β −β), (−β α −β), (−β −β α) ] (each row is in paranthesis) (c) Find the algebraic multiplicity and the geometric multiplicity of every eigenvalue of A. (d) Justify if the matrix A is diagonalizable.

If sec(α) = − 13 5 where π 2 < α < π and tan(β) =...

If sec(α) = − 13 5 where π 2 < α < π and tan(β) = 24 7 where π < β < 3π 2 , find the exact values of the following. (a) csc(α − β) (b) sec(α + β) (c) cot(α + β)

Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α <...

Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α < 1, satisfies all assumptions made in lecture 5. Assumptions: 1) Output increases when either the capital stock or the number of workers increase 2) Both the marginal product of capital and the marginal product of labor are decreasing 3) The marginal product of labor increases when capital increases, and the marginal product of capital increases when labor increases 4) For any constant x >...

4. Suppose a firm’s technology is described by a production function where the quantity produced is...

4. Suppose a firm’s technology is described by a production function where the quantity produced is equal to the square root of capital times labor (that is, Q = √(L●K) a. Using graph paper, draw the isoquant for output = 8 units. b. Suppose the firm has $128 to spend on its variable inputs and the price of L and K is $8. On the same graph on which you drew the isoquant, draw the isocost line. What is the...

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1....

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1. Let ? be the amount of labor, ? the amount of capital, and ? be the amount of other materials used. Let the profit function be defined by ?=?−(??+??+??) where the costs of labor, capital, and other materials are, respectively, ?, ?, and ?. Determine whether second order conditions for profit maximization hold, when the profit function is defined by ?=?−(30?+20?+10?) with ?=5?^0.3?^0.4?^0.2.

Let α, β be cuts as defined by the following: 1) α ≠ ∅ and α...

Let α, β be cuts as defined by the following: 1) α ≠ ∅ and α ≠ Q 2) if r ∈ α and s ∈ Q satisfies s < r, then s ∈ α. 3) if r ∈ α, then there exists s ∈ Q with s > r and s ∈ α. Let α + β = {r + s | r ∈ α and s ∈ β}. Show that the set of all cuts R with the...

Suppose the production function isY=AKαL1-α where A = 4 and α=0.4 (note: there is no change in technology since A is constant)

Suppose the production function isY=AKαL1-α where A = 4 and α=0.4 (note: there is no change in technology since A is constant). Assume the economy is in a steady state. The labor force growth rate n = 0.02, capital depreciation rate δ = 0.1, and savings rate s = 0.06. What is the capital per worker in the steady state according to the Solow model?

A firm’s production function is given by q = 40 ln(EW + EB + 1) where...

A firm’s production function is given by q = 40 ln(EW + EB + 1) where EW and EB are the number of whites and blacks employed by the firm, respectively. From this it can be shown that the marginal product of labor is MPE = 40 / (EW + EB + 1). Suppose the market wage for blacks is $50, the market wage for whites is $100, and the price of each unit of output is $20. (a) How...

9. a. Suppose that a firm’s production function is q=9x^1/2 in the short run, where there...

9. a. Suppose that a firm’s production function is q=9x^1/2 in the short run, where there are fixed costs of $1000, and x is the variable input whose cost is $4000 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). b. Write down the equation for the supply curve. c. If price is $1000, how many units will the firm produce? What is the level of...

Consider the model Et = α + β It + ut

Consider the model Et = α + β It + ut where ut has a zero mean Where Et is aggregate expenditure on a good and It is total income. Given the following information OLS Estimates Using 51 Observations Dependent Variable Et Variable Coeff STD error T Stat constant 0.26644 0.3294 .809 It 0.06754 .0035 19.288 SSR = 157.90709 Unadjusted R2 = 0.884 Adjusted R2 = .881 OLS Estimates Using 51 Observations Dependent Variable u2t...

Question