Q: If GDP per capita is given by $$\frac{Y}{L}$$, and $$L is $$the population, which equation correctly decomposes GDP per capita?

$$\frac{Y}{L} = \frac{N}{L} \times \frac{Y}{N}$$

Question 1

Which equation best represents the aggregate production function described in the study materials?

Accepted Answer

$$Y = A F(K, N)$$

Question 2

In the Cobb-Douglas production function $$Y = A K$$^{\alpha}$$ N$$^{1-\alpha}$$, what does the parameter $$\alpha$$ represent?

Accepted Answer

The share of capital in production

Question 3

Refer to the first image. If capital ($$K) is $$fixed and labor ($$N) $$increases from $$N_1 to$$ $$N_2$$, what happens to output ($$Y$$)?

Accepted Answer

Output increases, but by less than double

Question 4

Refer to the second image. Why is $$Y_3$$ - $$Y_2$$ less than $$Y_2$$ - $$Y_1$$ when labor increases successively?

Accepted Answer

Diminishing marginal productivity of labor

Question 5

What does the marginal product of labor (MPN) measure?

Accepted Answer

The increase in output from a small increase in labor, holding capital fixed

Question 6

Refer to the third image. What does the downward slope of the MPN curve indicate?

Accepted Answer

Diminishing marginal productivity of labor

Question 7

If total factor productivity ($$A) $$increases, what happens to the marginal products of capital and labor?

Accepted Answer

Both MPN and MPK increase

Question 8

Refer to the fourth image. What does the shift from point B to point C represent?

Accepted Answer

An increase in MPN due to higher TFP

Question 9

Which formula is used to decompose output growth into growth in productive factors and TFP?

Accepted Answer

$$\frac{\Delta Y}{Y} \approx \frac{\Delta A}{A} + \alpha \frac{\Delta K}{K} + (1-\alpha) \frac{\Delta N}{N}$$

Question 10

How can TFP growth be calculated if you have data on output, capital, labor, and capital share?

Accepted Answer

$$\frac{\Delta A}{A} \approx \frac{\Delta Y}{Y} - \alpha \frac{\Delta K}{K} - (1-\alpha) \frac{\Delta N}{N}$$

Question 11

If GDP per capita is given by $$\frac{Y}{L}$$, and $$L is $$the population, which equation correctly decomposes GDP per capita?

Accepted Answer

$$\frac{Y}{L} = \frac{N}{L} 	imes \frac{Y}{N}$$

Question 12

In the Cobb-Douglas production function, what is the formula for labor productivity ($$\frac{Y}{N}$$)?

Accepted Answer

$$\frac{Y}{N} = A \left( \frac{K}{N} \$$right)^{\alpha}$$

Question 13

If the fraction of the population in the labor force ($$\frac{N}{L}) $$does not have a trend, what is the main source of growth in GDP per capita?

Accepted Answer

Growth in labor productivity ($$\frac{Y}{N})$$

Question 14

Suppose a country doubles both its capital and labor inputs. If its production function exhibits constant returns to scale, what happens to output?

Accepted Answer

Output doubles

Question 15

Which of the following best describes a positive supply (productivity) shock?

Accepted Answer

An increase in total factor productivity ($$A) $$that shifts the production function upward

Question 16

If the marginal product of capital (MPK) declines as capital increases, what economic principle does this illustrate?

Accepted Answer

Diminishing marginal productivity of capital

Question 17

A firm increases its labor force while keeping capital fixed. According to the production function, what happens to the marginal product of labor (MPN)?

Accepted Answer

MPN decreases due to diminishing returns

Question 18

If a country experiences rapid TFP growth, what is the likely effect on its GDP per capita?

Accepted Answer

GDP per capita will increase, primarily due to higher labor productivity

Question 19

Which of the following is NOT a plausible reason for ignoring materials as an input in the aggregate production function?

Accepted Answer

Materials are less important than capital and labor in determining output

Production, Productivity, and Growth Accounting in Macroeconomics

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