# ECON 2400 Chapter Notes -Demand Curve, Real Interest Rate, Goes 15

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Published on 15 Apr 2013

Department

Economics

Course

ECON 2400

Professor

Questions for Review

1. The factors of production and the production technology determine the amount of out-

put an economy can produce. The factors of production are the inputs used to produce

goods and services: the most important factors are capital and labor. The production

technology determines how much output can be produced from any given amounts of

these inputs. An increase in one of the factors of production or an improvement in tech-

nology leads to an increase in the economy’s output.

2. When a firm decides how much of a factor of production to hire or demand, it considers how

this decision affects profits. For example, hiring an extra unit of labor increases output and

therefore increases revenue; the firm compares this additional revenue to the additional

cost from the higher wage bill. The additional revenue the firm receives depends on the

marginal product of labor (MPL) and the price of the good produced (P). An additional unit

of labor produces MPL units of additional output, which sells for Pdollars per unit.

Therefore, the additional revenue to the firm is P×MPL. The cost of hiring the additional

unit of labor is the wage W. Thus, this hiring decision has the following effect on profits:

ΔProfit = ΔRevenue – ΔCost

= (P×MPL) – W.

If the additional revenue, P×MPL, exceeds the cost (W) of hiring the additional unit of

labor, then profit increases. The firm will hire labor until it is no longer profitable to do

so—that is, until the MPL falls to the point where the change in profit is zero. In the

equation above, the firm hires labor until Δprofit = 0, which is when (P×MPL) = W.

This condition can be rewritten as:

MPL = W/P.

Therefore, a competitive profit-maximizing firm hires labor until the marginal product

of labor equals the real wage. The same logic applies to the firm’s decision regarding

how much capital to hire: the firm will hire capital until the marginal product of capital

equals the real rental price.

3. A production function has constant returns to scale if an equal percentage increase in

all factors of production causes an increase in output of the same percentage. For exam-

ple, if a firm increases its use of capital and labor by 50 percent, and output increases

by 50 percent, then the production function has constant returns to scale.

If the production function has constant returns to scale, then total income (or

equivalently, total output) in an economy of competitive profit-maximizing firms is

divided between the return to labor, MPL ×L, and the return to capital, MPK ×K. That

is, under constant returns to scale, economic profit is zero.

4. A Cobb-Douglas production function function has the form

F(K,L)

=

AK

α

L

1–α. The text

showed that the parameter αgives capital’s share of income. (Since income equals out-

put for the overall economy, it is also capital’s share of output.) So if capital earns one-

fourth of total income, then a= 0.25. Hence,

F(K,L)

=

AK

0.25

L

0.75.

5. Consumption depends positively on disposable income—the amount of income after all

taxes have been paid. The higher disposable income is, the greater consumption is.

The quantity of investment goods demanded depends negatively on the real inter-

est rate. For an investment to be profitable, its return must be greater than its cost.

Because the real interest rate measures the cost of funds, a higher real interest rate

makes it more costly to invest, so the demand for investment goods falls.

11

CHAPTER 3National Income: Where It Comes From

and Where It Goes

6. Government purchases are a measure of the dollar value of goods and services pur-

chased directly by the government. For example, the government buys missiles and

tanks, builds roads, and provides services such as air traffic control. All of these activi-

ties are part of GDP. Transfer payments are government payments to individuals that

are not in exchange for goods or services. They are the opposite of taxes: taxes reduce

household disposable income, whereas transfer payments increase it. Examples of

transfer payments include Social Security payments to the elderly, unemployment

insurance, and veterans’ benefits.

7. Consumption, investment, and government purchases determine demand for the econo-

my’s output, whereas the factors of production and the production function determine

the supply of output. The real interest rate adjusts to ensure that the demand for the

economy’s goods equals the supply. At the equilibrium interest rate, the demand for

goods and services equals the supply.

8. When the government increases taxes, disposable income falls, and therefore consumption

falls as well. The decrease in consumption equals the amount that taxes increase multi-

plied by the marginal propensity to consume (MPC). The higher the MPC is, the greater is

the negative effect of the tax increase on consumption. Because output is fixed by the fac-

tors of production and the production technology, and government purchases have not

changed, the decrease in consumption must be offset by an increase in investment. For

investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a

decrease in consumption, an increase in investment, and a fall in the real interest rate.

Problems and Applications

1. a. According to the neoclassical theory of distribution, the real wage equals the mar-

ginal product of labor. Because of diminishing returns to labor, an increase in the

labor force causes the marginal product of labor to fall. Hence, the real wage falls.

b. The real rental price equals the marginal product of capital. If an earthquake

destroys some of the capital stock (yet miraculously does not kill anyone and lower

the labor force), the marginal product of capital rises and, hence, the real rental

price rises.

c. If a technological advance improves the production function, this is likely to

increase the marginal products of both capital and labor. Hence, the real wage

and the real rental price both increase.

2. A production function has decreasing returns to scale if an equal percentage increase in

all factors of production leads to a smaller percentage increase in output. For example,

if we double the amounts of capital and labor, and output less than doubles, then the

production function has decreasing returns to scale. This may happen if there is a fixed

factor such as land in the production function, and this fixed factor becomes scarce as

the economy grows larger.

A production function has increasing returns to scale if an equal percentage

increase in all factors of production leads to a larger percentage increase in output. For

example, if doubling inputs of capital and labor more than doubles output, then the pro-

duction function has increasing returns to scale. This may happen if specialization of

labor becomes greater as the population grows. For example, if only one worker builds

a car, then it takes him a long time because he has to learn many different skills, and

he must constantly change tasks and tools. But if many workers build a car, then each

one can specialize in a particular task and become very fast at it.

3. a. A Cobb–Douglas production function has the form Y= AKαL1 – α. The text showed

that the marginal products for the Cobb–Douglas production function are:

MPL = (1 – α)Y/L.

MPK = αY/K.

12 Answers to Textbook Questions and Problems

Competitive profit-maximizing firms hire labor until its marginal product

equals the real wage, and hire capital until its marginal product equals the real

rental rate. Using these facts and the above marginal products for the

Cobb–Douglas production function, we find:

W/P = MPL = (1 – α)Y/L.

R/P = MPK = αY/K.

Rewriting this:

(W/P)L= MPL ×L= (1 – α)Y.

(R/P)K= MPK ×K= αY.

Note that the terms (W/P)Land (R/P)Kare the wage bill and total return to capi-

tal, respectively. Given that the value of α= 0.3, then the above formulas indicate

that labor receives 70 percent of total output (or income), which is (1 – 0.3), and

capital receives 30 percent of total output (or income).

b. To determine what happens to total output when the labor force increases by 10

percent, consider the formula for the Cobb–Douglas production function:

Y= AKαL1 – α.

Let Y1equal the initial value of output and Y2equal final output. We know that

α= 0.3. We also know that labor Lincreases by 10 percent:

Y1= AK0.3L0.7.

Y2= AK0.3(1.1L)0.7.

Note that we multiplied Lby 1.1 to reflect the 10-percent increase in the labor

force.

To calculate the percentage change in output, divide Y2by Y1:

=

= (1.1)0.7

= 1.069.

That is, output increases by 6.9 percent.

To determine how the increase in the labor force affects the rental price of

capital, consider the formula for the real rental price of capital R/P:

R/P = MPK = αAKα– 1L1 – α.

We know that α= 0.3. We also know that labor (L) increases by 10 percent. Let

(R/P)1equal the initial value of the rental price of capital, and (R/P)2equal the

final rental price of capital after the labor force increases by 10 percent. To find

(R/P)2, multiply Lby 1.1 to reflect the 10-percent increase in the labor force:

(R/P)1= 0.3AK –0.7

L0.7.

(R/P)2= 0.3AK – 0.7(1.1L)0.7.

The rental price increases by the ratio

=

= (1.1)0.7

= 1.069.

So the rental price increases by 6.9 percent.

Chapter 3 National Income: Where It Comes From and Where It Goes 13

AK0.3(1.1L)0.7

AK0.3L0.7

Y2

Y1

0.3AK –0.7(1.1L)0.7

0.3AK –0.7L0.7

(R/P)2

(R/P)1

## Document Summary

C h a p t e r 3 national income: where it comes from and where it goes. Questions for review: the factors of production and the production technology determine the amount of out- put an economy can produce. The factors of production are the inputs used to produce goods and services: the most important factors are capital and labor. The production technology determines how much output can be produced from any given amounts of these inputs. For example, hiring an extra unit of labor increases output and therefore increases revenue; the firm compares this additional revenue to the additional cost from the higher wage bill. The additional revenue the firm receives depends on the marginal product of labor (mpl) and the price of the good produced (p). An additional unit of labor produces mpl units of additional output, which sells for p dollars per unit. Therefore, the additional revenue to the firm is p mpl.