Question

Let us assume a neoclassical economy with two factors of production: Capital and Labor. Y=AK*2/3L*1/3. a) (5 points) Derive an equation for the marginal product of labor. b) (5 points) Suppose that immigration increases the labor force by 20 percent. How much does the rental price of capital change? c) (5 points) Given the equilibrium nominal wage and price level, W = 4 and P = 2, and A = 8 and K = 8 find the amount of labor, i.e. L=?

Answer #1

1. Use the neoclassical theory of distribution to predict the
impact on the real wage and the real rental price of capital of
each of the following event:
a. A wave of immigration increases the labor force.
b. An earthquake destroys some of the capital stock.
c. A technological advance improves the production function.
d. High inflation doubles the prices of all factors and outputs
in the economy.

Suppose the firm's production function is Q = K 1/3L 2/3 . a. If
the rental rate of capital R = $30 and the wage rate W = $40, what
is the cost-minimizing capital-to-labor ratio? b. If the rental
rate of capital R is $35 and the wage rate W is $70, how many units
of labor and capital should the firm use to produce 12 units of
output?

Suppose an economy's production is defined by the following
neoclassical production function: Y=3K 1/3L
2/3. Suppose further that the economy wide supply of
capital and labor are given as 125,000 and 1,000 respectively. If
congress imposes a minimum wage of 11 units of output in this
economy, what will be the likely result of this action?
a. An unemployment rate of 25%
b. An unemployment rate of 10%
c. Full employment, but lower output
d. An unemployment rate of 50%

Consider an economy that uses two factors of production, capital
(K) and labor (L), to produce two goods, good X and good Y. In the
good X sector, the production function is X = 4KX0.5 + 6LX0.5, so
that in this sector the marginal productivity of capital is MPKX =
2KX-0.5 and the marginal productivity of labor is MPLX = 3LX-0.5.
In the good Y sector, the production function is Y = 2KY0.5 +
4LY0.5, so that in this sector...

Suppose an economy's production is defined by the following
neoclassical production function: Y=50K 1/3L
2/3. Suppose further that the economy wide supply of
capital and labor are given as 125 and 64. What happens to output
per worker if there is a war that destroys half the capital in the
economy?
Output per capital falls to half the initial level
Output per capita falls to less than half the initial level
Output per capita falls to more than half the...

2. Use the specific-factors model to answer question 2. Assume
that there are two industries, food and cloth. The food industry
uses labor and land as inputs while the cloth industry uses labor
and capital as inputs. The marginal product of labor in both
industries is as follows:
Marginal Product of Labor
Labor
Cloth
Food
0
1.4
1.6
1
1.3
1.5
2
1.2
1.4
3
1.1
1.3
4
1
1.2
5
.9
1.1
6
.8
1
7
.7
.9...

Assume that a competitive economy can be described by a
constant-returns-to-scale Cobb-Douglas production function and all
factors of production are fully employed. Holding other factors
constant, including the quantity of capital and technology,
carefully explain how a one-time, 10 percent increase in the
quantity of labor as a result of a special immigration policy, will
change the following: (12 points)
The level of output produced
The real wage of labor
The real rental price of capital
Labor share of total...

1) Which
of these factors would shift the labor demand curve out (increase
labor demand)?
a) Decrease in
immigration into the United States.
b) Increase in
immigration into the United States
c) Price of output
good increases (labor is used to make this output).
d) Price of output
good decreases (labor is used to make this output).
2) If the
marginal revenue product of labor is greater than the wage rate
(M RPh > w), what should a
profit maximizing...

Consider the following data on quantities of two factors,
capital and labor, available, and their use to produce a unit of
each of the two goods, cloth and food: K = 3000,
L = 2000, aKC = 2,
aLC= 2, aKF = 3,
aLF = 1.
a. Derive equations for
PC and PF. Now solve the
equations for w (wage rate) and r (capital rental
rate). (No need to write the expressions on the answer space
provided). Answer the following questions...

1. Labor Market
Consider an economy with production function given by Y =
AK0.5L0.5 where A is the total factor productivity (TFP), K is the
capital stock and L is the labor input. For simplicity assume
capital is fixed and equal to 1. Assume A=150.
Write the firm’s problem of choosing labor demand. Derive the
demand for labor as a function of the real wage.
Assume labor supply is inelastic and fixed at L̄ = 100. Find the
equilibrium values...

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