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EXAM IN MACROECONOMICS INTERMEDIATE LEVEL AT KARLSTAD
UNIVERSITY, SPRING 2008.
Maximum points: 25 points. To pass 12.5 points are required.
1. 12 points Use the overlapping generation model with the following production function:
Y  AK  L1 , and the following utility function: U  cyt  cot11
Assume also that the growth rate in A is zero. Assume that the world consists of 2 economies:
Savum and Spendum.
Parameter
SAVUM SPENDUM EFFICIENT
A
4
4
16
0.5
0.6
0.6

0.5
0.5
0.5

Population growth
0.1
0.1
0.1
rate (n)
N(0)
100
200
-1a. calculate the long-run equilibrium values for capital per worker (k=K/L), consumption per
person when being young (cy), production per worker (y=Y/L), the real wage per worker (W),
and the real return on capital for the two countries: SAVUM and SPENDUM.
1b. Calculate long-run GDP (Y) for the 2 countries: SAVUM AND SPENDUM. Explain.
If you cannot answer with numbers, explain in words which country has higher or lower
values on the variables mentioned above in 1a. and 1b. for partial credit.
c. If we allow for capital mobility (K) between the countries, from what country (SAVUM
and SPENDUM) will the capital move? Why? Does capital mobility diminish initial
differences in k,y,W, and real return on capital?
2a. Assume another country: EFFICIENT. Under the assumption that this country is a closed
economy calculate capital per worker (k), production per worker (y=Y/L), consumption per
worker, real wage per worker, and the real rental price per unit of capital.
2b. If now assuming 2 countries: SPENDUM and EFFICIENT, and allowing for capital
mobility (K) between these 2 countries. (Note: The country SAVUM does not exist any
longer.) Do you expect capital to move between the countries SPENDUM and EFFICIENT?
Explain.
If you cannot answer with numbers, explain in words which country has higher or lower
values on the variables for partial credit.
answers:
K=((1-alpha)*(1-beta)A/(1+n))^2
Y=Ak^0.5
W=beta*y=0.5*y
Cy=apfa*y
r=A*beta*k^-0.5
SAVUM
0.826
3.636
1.818
1.818
2.200
SPENDUM
0.529
2.909
1.4546
1.7454
2.749
EFFICIENT
8.463
46.55
23.275
27.93
2.749
3. 4 poiints. What is the effect on the long-run equilibrium values of k, y, consumtion when
being young and consumption when being old, the real wage, and the real return on capital if
n increases? No need to calculate with numbers. Who tend to welcome immigration and
whom tend to oppose immigration of workers and employer? Explain why.
4. 4 points If the government tax the old, can it actually increase production per capita relative
to the case when there is no government? Use our overlapping generations model and explain
why.
5. 2.5 points write the government’s intertemporal budget constraint.
6. 2.5 points Mention and explain two reasons why inequality may impact the growth rate of
per capita income according to the article by Barro.