14.02 Principles of Macroeconomics

## Problem Set #2

Posted: Wednesday, February 21, 2001

Due Date: Wednesday, February 28, 2001

Part I: True/False Questions (Briefly explain your answer.)  Note that all of the points in this section are for the explanations, not for just stating “true” or “false.”  (26 points)

1. (9 points)  The following increase productivity:

(a)    on-the-job training

(b)   higher education

(c)    working extra hours

(d)   an increase in the wage rate

(e)    higher pensions

(f)     higher retirement age

(g)    higher labor force participation rate

(h)    higher gross investment

(i)      higher saving rate.

[Answer T/F and give a brief reason for each section separately.]

1. (4 points)  The following increase growth:

(a)    higher unemployment

(b)   lower investment share of GDP

(c)    lower high school enrollment

[Answer T/F and give a brief reason for each section separately.]

1. (4 points)  The United States’ GDP in 1998 was 16 times higher than its GDP in 1960.  Further, in spite of the Great Depression, the US output was higher in 1940 than in 1929.
2. (4 points)  Okun’s Law states that the reduction of 1% in unemployment requires an increase of 0.5% in inflation.
3. (5 points)  It is possible that France, Germany and Japan all experience growth rates higher than the US, yet the most important technical advances be made in the US.

Part II: National Accounts  (20 points – 4 points each)

Suppose you are measuring annual US GDP by adding up the final value of all goods and services produced in the economy.  Determine the effect of each of the following transactions on GDP:

1. You buy \$100 worth of fish from a fisherman, which you cook and eat at home.
2. A seafood restaurant buys \$100 worth of fish from a fisherman.
3. Delta Airlines buys a new jet from Boeing for \$200 million.
4. The Greek national airline buys a new jet from Boeing for \$200 million.
5. Delta Airlines sells one of its jets to John Travolta for \$100 million.

Part III: Growth Theory  (See chapter 10-3 in Blanchard; 26 points)

Assume the following production function:

Y = F (K,N)

While Y = Output, K = Capital, and N = Number of workers.

1. (8 points) What does it mean if the production function demonstrates constant returns to scale?  Can it, at the same time, demonstrate decreasing returns to capital?
2. (5 points) Assume that the above production function has constant returns to scale.  Derive output per worker as function of capital per worker.
3. (5 points) Draw a graph of the above relationship, with output per worker on the vertical axis.  What is a reasonable assumption should you make regarding the return to factors?
4. (8 points) How would the above curve shift in response to

(a)    an improvement in technology

(b)   an increase in education

(c)    an earthquake

(d)   an increase in immigration?

Part IV: The Saving Paradox  (28 points)

### Consider the following model of closed economy (from last PS#1):

C = 50 + 0.6(Y-T)

I= 10 + 0.1Y - i

G=100

### T=100

X=M=0

1. (4 points)  Write down private saving and government saving in this economy.
2. (6 points) Show how we can re-write the equilibrium condition for GNP (used in problem set 1) as a relationship between investment and total saving, and give a brief explanation of what it means.
3. (6 points)  Solve the above equilibrium condition for output, assuming i=10. What is the marginal propensity to save (MPS)?
4. (12 points)  What happens to the equilibrium level of output, private saving and government saving if the MPS increases to 0.5? How would you reconcile your results with the common wisdom that a higher savings rate increases output?