Exam #1 Review Questions (ECNS 303)

February 17, 2015

(Note: These review questions do not necessarily comprise a comprehensive review for the

exam. Also study your lecture notes, quizzes, etc., to be fully prepared.)

1.) Exogenous vs. Endogenous variables

Consider a potential criminal. The individual maximizes his or her utility by choosing how much labor to supply

towards legitimate work opportunities (Lw) and how much labor to supply towards crime (Lc). In doing so, this

person can earn a wage w in the legal labor market and a return to crime n in the illegal labor market. In the illegal

labor market, the potential criminal faces costs of punishment (e.g. time in jail) C with a positive probability of

apprehension P. Of course, this individual must maximize subject to a time and budget constraint (but let’s not

worry about that for now). Categorize the variables listed above as either endogenous or exogenous to our utility

maximization model.

2.) GDP, GDP Deflator, and the Consumer Price Index

Consider a country that produces only two products: computers and automobiles. Sales and price data for these two

products for two different years are as follows:

#computers Price # automobiles Price

Year sold per computer sold per automobile

2000 500,000 $6,000 1,000,000 $12,000

2010 5,000,000 $2,000 1,500,000 $20,000

a.) Calculate nominal GDP in 2000 and 2010.

b.) Calculate real GDP in 2010 using 2000 as the base year.

c.) Calculate the GDP deflator in 2010.

d.) Calculate the CPI in 2010 using 2000 as the base year.

3.) National Income Accounting

a.) What are the 4 components of GDP

b.) Assume the economy is described by the following equations:

( , ) 1,200

125 0.75( )

( ) 200 10

150

100

Y Y F K L

Y C I G

C Y T

I I r r

G G

T T

Given the above equations, solve for the value of savings (S) and the real interest rate (r).

c.)Manipulate the savings equation to separate the saving of the private sector from that of government.

4.) Cobb-Douglas Production Function

Consider the Cobb-Douglas production function

F(K,L) = AKαL(1-α)

Show that the MPL is proportional to output per worker.

5.) Solow Growth Model

Consider an economy described by the production function:

Y = F(K,L) = K0.3L0.7

a.) What is the per-worker production function?

b.) Assuming no population growth or technological progress, find the steady-state capital stock per worker, output

per worker, and consumption per worker as a function of the saving rate and the depreciation rate.

6.) Golden Rule Steady State

Suppose the following national income accounts identity describes the economy

y = c + i

a.) Solve for the condition that describes the Golden Rule.

b.) Consider the decision a policymaker faces when choosing a steady-state that maximizes consumption per worker.

Suppose output per worker is governed by the following production function

y = k1/2

Also suppose that depreciation is 10% of capital. The policymaker must choose a savings rate s to accomplish his

goal. Further suppose the policymaker must choose between the following savings rates: 0.2, 0.5, and 0.8. Which

of the three savings rates maximizes consumption?

7.) Population Growth

Population growth gives us another explanation for why some countries are rich and others are poor. Show

graphically and explain the implications of an increase in the population growth rate in the Solow model.

8.) The Marginal Product of Capital

In Chapter 3 (National Income) of the textbook, the marginal product of capital was defined as the amount by which

total output changes when capital rises by 1 unit, or MPK = dY/dK. In Chapter 8 (Economic Growth), MPK is

equal to the amount by which output per effective worker rises when capital per effective worker rises by 1 unit, or

MPK = df(k)/dk, where k = K/EL. Show the two definitions are the same.

9.) Equilibrium interest rate (this is #10 from Ch. 3)

Consider an economy described by the following equations

Y = C + I + G

Y = 5000

G = 1000

T = 1000

C = 250 + 0.75(Y – T)

I = 1000 – 50r

a.) In this economy, compute private saving, public saving, and national saving.

b.) Find the equilibrium interest rate.

c.) Now suppose that G rises to 1250. Compute private saving, public saving, and national saving.

d.) Find the new equilibrium interest rate.

10.) Cobb-Douglas Production Function (this is #1 from Ch. 8)

Country A and country B both have the production function

Y = F(K, L) = K1/2L1/2

a.) Does this production function have constant returns to scale?

b.) What is the per-worker production function, y = f(k)?

c.) Assume that neither country experiences population growth nor technological progress and that 5 percent of

capital depreciates each year. Assume further that country A saves 10% of output and Country B saves 20% of

output each year. Using your answer from part (b) and the steady-state condition that investment equals

depreciation, find the steady-state level of capital per worker for each country. Then find the stead-state levels of

income per worker and consumption per worker.

d.) Suppose that both countries start off with a capital stocker per worker of 2. What are the levels of income per

worker and consumption per worker? Remembering that the change in the capital stock is investment less

depreciation, use a calculator or a computer spreadsheet to show how the capital stock will evolve over time in both

countries. For each year, calculate income per worker and consumption per worker. How many years will it be

before the consumption in country B is higher than the consumption in country A? (Note: On an exam, I will not

ask you to carry this procedure out to as many iterations as this problem requires…but, this is still good practice).

11.) Postwar growth (this is #2 from Ch. 8)

In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital

stock is destroyed in a war. By contrast, suppose that a war does not directly affect the capital stock, but that

casualties reduce the labor force. Assume the economy was in a steady state before the war, the saving rate is

unchanged, and the rate of population growth after the war is the same as it was before.

a.) What is the immediate impact of the war on total output and on output per person?

b.) What happens subsequently to output per worker in the postwar economy? Is the growth rate of output per

worker after the war smaller or greater than it was before the war?

12.) Solow model plus unemployment (this is part (a) from #8 in Ch. 8)

Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to

the production function Y = Kα[(1 – u)L]1-α, where K is capital, L is the labor force, and u is the natural rate of

unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate δ.

a.) Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of

unemployment. Also, solve for the steady-state values of k and y.

b.) Suppose that some change in government policy reduces the natural rate of unemployment. Describe how this

change affects output both immediately and over time. You may use a graph (although it is not necessary for this

problem) to support your answer.

13.) Solow model with technological progress (this is parts (a) and (b) from #1 in Ch. 9)

Suppose an economy described by the Solow model has the following production function:

Y = K1/2(LE)1/2

a.) For this economy, what is f(k)? Use your answer to part (a) to solve for the steady-state value of y as a function

of s, n, g, and δ.

b.) Two neighboring economies have the above production function, but they have different parameter values.

Atlantis has a saving rate of 28 percent and a population growth rate of 1 percent per year. Xanadu has a saving rate

of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and δ = 0.04. Find the

steady-state value of y for each country

14.) More on the Solow model with technological progress (this is #2 from Ch. 9)

In the United States, the capital share of GDP is about 30%, the average growth in output is about 3% per year, the

depreciation rate is about 4% per year, and the capital-output ratio is about 2.5. Suppose that the production

function is Cobb-Douglas, so that the capital share in output is constant, and that the United States has been in a

steady state.

a.) What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy=(δ + n + g)k]

b.) What is the marginal product of capital in the initial steady state?

c.) Suppose that public policy raises the saving rate so that the economy reaches the Golden Rule level of capital.

What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal produce at the

Golden Rule steady state to the marginal product in the initial steady state. Explain.

d.) What will the capital-output ratio be at the Golden Rule steady state? [Hint: For the Cobb-Douglas production

function, the capital-output ratio is related to the marginal product of capital].

e.) What must the saving rate be to reach the Golden Rule steady state?