ECO3203 Chapter 4

What is the marginal product of capital (MPK) for the production function Y= Ak^(1/2)l^(1/2)?

(1/2)[Ak^(1/2)l^(1/2)/k]

Suppose India has a per capita GDP that is 0.074 times the United States GDP. It has a capital-per-person ratio that is 0.035 times that of the United States. Compared to the United States, the implied value of total factor productivity for India is approximately

0.23.

With a Cobb-Douglas production function y= k^(1/3)l^(2/3), the marginal product of capital is ________ and the marginal product of labor is ________.

MPK = (1/3)(Y/K); MPL = (2/3)(Y/L)

The solution to the firm's profit maximization is:

MPL = w and MPK = r.

Consider Figure 4.1. The shape of this production function suggests:

a diminishing marginal product of capital.

The equation Y= F(K,L)= Ak6(1/3)l^(2/3) is an example of :

a production function.

In the production model from the text, which of the following is NOT an exogenous variable or a parameter? The supply of capital The supply of labor The amount of capital The productivity parameter

The amount of capital

Which of the following is included in TFP? The amount of labor The amount of capital The quality of labor All of these choices are correct.

The quality of labor

Consider a perfectly competitive economy with a production function Y= Ak^(1/3)l^(2/3). There are 27 workers who produce cream cheese (a numéraire good) with 125 units of capital. If the productivity parameter is equal to 1 and the economy produces 40 tons of cream cheese in equilibrium, what is the sum of the total payments to capital and labor?

40 tons of cream cheese

The equation MPK = r* yields the:

optimal amount of capital, K*, a firm fires.

If MPK > r, the firm:

should hire more capital until MPK = r.

Output per person is higher when a country is more efficient in adopting a technology. a country has a higher capital-to-population ratio. a country has stronger property rights and contract enforcement. All of these choices are correct.

All of these choices are correct.

In a Cobb-Douglas production function, the factor share of income going to each input is equal to the exponent on the input in the production function. T/F

True

You plot the production function for the United States on a graph with output per person on the vertical axis and capital per person on the horizontal axis. If a shock occurs causing the productivity parameter to increase, the production function would shift upward. T/F

True

If the production function is given by y= k^(1/3)l^(2/3) and K = 27 and L = 8, total output equals:

Y = 12

According to Figure 4.5, does the production model accurately predict the level of per capita GDP for Singapore?

Yes, because the predicted value of per capita GDP for Singapore is close to the actual value of its per capita GDP

Consider Figure 4.3. The shape of this production function suggests:

a constant marginal product of capital.

The marginal product of the labor curve represents the:

demand for labor.

In Figure 4.4, MPL represents the labor ________, represents the labor ________, and the intersection of the two yields the ________.

demand; supply; equilibrium wage

A production function exhibits increasing returns to scale when you:

double each input—you more than double the output.

A production function has inputs X, Y, and Z and a productivity parameter A. The production function exhibits A^(1/3)X^(1/3)Y^(1/3)Z^(1/3)

constant returns to scale.

One of the key characteristics of the Cobb-Douglas production function is:

constant returns to scale.

The standard replication argument implies that Italy can raise its per capita GDP by doubling the amount of capital per person. T/F

False

We cannot tell whether the production function Y = K^(a)L^(1-a) has constant returns to scale, because we do not know the value of a. T/F

False

If MPL < w, the firm:

should fire some labor until MPL = w.

The marginal product of labor is defined as:

the additional output generated by hiring an additional unit of labor.

If MPK = r, the firm:

has the optimal amount of capital.

Consider two economies. If each country has the same production function and the same amount of capital and labor, the country that ________ produces more.

is more productive

Output per capita and output per worker are

equal in the production model, but output per capita is smaller in general.

In a production model where the production function y= Ak^(1/3)l^(2/3) is the equilibrium wage rate is equal to , labor supply is 30/27 workers and the productivity parameter is equal to 1. What is the equilibrium level of capital?

125 30/27 = (2/3)[k^(1/3)27^(2/3)/27] K= 125

Consider an economy characterized by the production function y= Ak^(1/2)l^(1/2) where the productivity parameter is equal to 1.2. How many units of output can be produced with 25 units of capital and 64 workers?

48

A firm uses capital and labor to produce a good. Which of the following is greatest? Accounting profit. Economic profit. It depends on the situation. All the choices are equal.

Accounting profit.

If the productivity parameter is assumed to equal 1, the production model correctly identifies that countries are richer if they have more capital. incorrectly predicts that poor countries are substantially richer than they are. incorrectly predicts that some countries are richer than the United States. All of these choices are correct.

All of these choices are correct.

Capital per person explains about one-half of the difference in per capita income between the richest and poorest countries. T/F

False

If the marginal product of capital is less than the rental rate of capital, the firm should rent more capital. T/F

False

The firm's profit maximization problem is:

max π = F(K, L) − rK − wL{K, L}.

If k= K and l=L, then output is determined by:

the total amount of capital and labor available in an economy.