4. Suppose that an economy's production function is Cobb-Douglas with parameter a=0.3. a. What fractions of...

4. Suppose that an economy's production function is Cobb-Douglas with parameter a=0.3.

a. What fractions of income do capital and labor receive?

b. Suppose that immigration increases the labor force by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

c. Suppose that a gift of capital from abroad raises the capital of stock by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

Expert Solution

a. What fractions of income do capital and labor receive?
Solution: Fractions of income capital = 0.3 or 30%
Fractions of income labor = 0.7 or 70%

b. Suppose that immigration increases the labor force by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?
Total output grows at the rate of 6.9% or 1.068993
The rental price of capital grows at the rate of 6.89%
The real wage grows at the rate of -2.819%
Working: Enclosed

c. Suppose that a gift of capital from abroad raises the capital of stock by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?
Total output grows at the rate of 2.9% or 1.029006
The rental price of capital grows at the rate of -6.4%
The real wage grows at the rate of 2.9%
Working: Enclosed

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?
Total output grows at the rate of 10%
The rental price of capital grows at the rate of 10%
The real wage grows at the rate of 10%

Rahul Sunny answered 1 year ago

3. Suppose that the production function is CobbDouglas with parameter α = 0.3. a. What fractions...

3. Suppose that the production function is CobbDouglas with parameter α = 0.3. a. What fractions of income do capital and labour receive? b. Suppose that immigration raises the labour force by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? c. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?...

Consider an economy with the following Cobb-Douglas production function:

Chapter 7, Labor Market Regulation (3 points):• Consider an economy with the following Cobb-Douglas production function:Y =k^1/3L^2/3The economy has 1,000 units of capital and a labor force of 1,000 workers.(a) Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock (Hint: Review Chapter 3.)(b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...

Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the...

Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among workers). Markets for output and factors of production are both competitive. The production function is Y = K^1/3*L^1/3*H^1/3 1. Prove that this technology shows constant returns to scale. 2. Solve the competitive firm’s profit maximization problem by deriving the first-order conditions. 3. An...

Suppose a firm has a Cobb-Douglas production function. Show graphically that an increase in the rental...

Suppose a firm has a Cobb-Douglas production function. Show graphically that an increase in the rental rate of capital will increase the amount of labor hired if production remains at the same amount(10pts).

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time,...

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time, derive the conditional input demands ? ∗ (?, ?, ?) and ? ∗ (?, ?, ?) and the associated long-run cost function ?(?, ?, ?) under the assumption that ? + ? = 1. b) Describe the average cost and marginal cost functions. How do they depend on output q and factor prices w and r? Explain. c) Continuing to assume ? + ?...

3. Suppose that you have a Cobb-Douglas production function of the following form: Y = 0.25K0.24L...

3. Suppose that you have a Cobb-Douglas production function of the following form: Y = 0.25K0.24L 0.40D 0.10 (1) where Y is output, K is capital stock, L is labour, and D is land. (a) What is the interpretation of the individual exponents on K, L and D respectively? (b) What is the interpretation of the sum of these coefficients (i.e., which represents the degree of homogeneity for this function)? Is this function subject to constant, decreasing or increasing returns...

Suppose that you have a standard Solow model with production given by Cobb-Douglas function. Assume A...

Suppose that you have a standard Solow model with production given by Cobb-Douglas function. Assume A = 1, s = 0.1, α = 1/3, and δ = 0.1. Solve for the steady-state level of capital per worker, k* (Hint: use dynamic formula for capital stock.). Create an Excel spreadsheet to compute the dynamics of the capital stock. Plot the evolution of capital stock for 10 periods (i.e., t = 1, 2, … , 10) using your result in part (a)....

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.

A certain firm in the beverage industry is faced with the following Cobb-Douglas production function of...

A certain firm in the beverage industry is faced with the following Cobb-Douglas production function of Q left parenthesis L comma K right parenthesis equals 4 L to the power of 0.3 end exponent space K to the power of 0.5 end exponent a) What is A P subscript L and APK? [6 marks] b) What is the level of M P subscript L space end subscript and M P subscript K when K = 40 and L = 40...

Question