4 points
1. Analyze the following statement:
” A higher level of production (GDP) inevitably leads to a deterioting environmental quality”.
Deterioting means worse.
Is there a difference between local pollution or global pollution? If so explain, why?
By local pollution I mean pollution that primarily affect the local community such as smoke
in the air and pollution in rivers and lakes. Global pollution on the other hand is pollution that
affect the environment around the world regardless where it is emitted. For example, carbon
dioxide (CO2) contributes to the green house effect regardless where the carbon dioxide is
emitted; Sunne or Cairo.
10 points
2. Assume an economy, which is described by the life-cycle model for a closed economy. To
simplify assume that the growth rate of the technology is zero; that is, A / A =0, and that the
growth rate of the size of the young generation (n) is zero.
Suppose that utility and production are described by the usual Cobb-Douglas functions:
Yt  A  Kt  L1t  ; Ut  cyt  c1ot1 and that the following parameter values hold:
Parameter
A
a.
b.
c.
d.
e.
Value
4
0

0.5

N
100
Calculate the steady-state capital-labor ratio and the level of output.
Suppose that the government decides to purchase 1 unit of output for government
consumption each period. To pay for it, the government collects taxes equal to 1 from
the old each period. What will the steady-state capital-labor ratio and output level be?
Compare these answers to those calculated in a. Explain any differences or
similarities.
Now suppose that the government changes its policy and pays for its spending by
collecting taxes equal to 1 from the young each period. Calculate the capital-labor
ration and the output level for the 2 periods following the change. Compare these
answers to the steady state values calculated in part b. Explain any differences or
similarities.
If the old (due to altruism) compensate the young by a transfer of 1, what is the effect
on capital-labor and the output level. Compare these answers to the steady state values
calculated in part b. Explain any differences or similarities.
Now disregard the possibility of voluntary transfers from old to young. Suppose that
the government continues to collect taxes equal to 1 from the young each period. Now,
however, the government uses the tax revenue to purchase 0.5 units of capital and 0.5
unit of consumption instead of 1 unit of consumption. What will be the impact of the
policy change on the capital-labor ratio and output level in the 2 periods after the
change? Do these differ from the values calculated in part c. Why or why not?
Svar:
1/(1  )
4
A. k   (1   ) A
y  Ak   4  2  8
B. same effect as in A.
C. k1   (1   ) A k0  1  2  40.5  1  4  1  3
k2   (1   ) A k1  1  2  30.5  1  3.46  1  2.46
y1  Ak1  4  3  6.93
y2  Ak2  4  2.46  6.27
C. same effect as in A and B.
E. k1   (1   ) A k0  0.5  2  40.5  0.5  4  0.5  3.5
k2   (1   ) A k1  1  2  3.50.5  .5  3.74  0.5  3.24
y1  Ak1  4  3.5  7.48
y2  Ak2  4  3.24  7.2
7 points
3. Labor supply and saving, the effect of a lower pension in the future.
Use the life-cycle model and assume that an individual lives 2 periods. In the first period she
works and consumes, in the second period she also consumes. In this period she is retired.
While working in the first period, she values leisure. Assume the following utility function:
where 0    1 , 0    1 , 0  (1     )  1 .
U  C1  C2  R11 
where C1 is good consumption in period 1 when she is young and works, C2 is good
consumption in period 2 when she is retired, and R1 is leisure that the individual enjoys in
period 1. In the second period the individual is not allowed to work. As a result she faces no
choice between labor and leisure in this period. The time constraint in period 1 is: L+R1=1.
If the individual uses all her time in period 1 (=1) to work, she receives the real wage w.
In this case, R1=0. The individual also receives an income that is not job-related, N1 (which
can be negative), in the first period and the non-work-related income (pension), N 2 , in the
second period.  and  are preference parameters. (The price of good consumption in the
first period is assumed to be 1 as usual.)
A.Write up the individual’s intertemporal budget constraint in terms of present value.
B.Derive the optimal demands of C1, C2, and R1 as functions of the exogenous variables:
w, r (=the real interest rate), N1 och N 2 . Derive also the optimal labor supply.
C.(i)Analyze the effect on C1, C2, R1 and L if N 2 decreases?
In other words, what happens if the individual expect to receive a lower pension in the
future?
(ii) What happens to optimal levels of C1, C2, R1 and L when r increases?
Instruction how to solve this problem: In case of a Cobb-douglas utility function (like the one
above), the share of expenditures on each good equals that good’s preference parameter in the
utility function. For example: If the individual maximizes U ( x, y )  x   y 
subject to the budget constraint: p x  x  p y  y  I
where y= quantity of good y, x=quantity of good x, p x = price of good x. p y = price of good
y. I = income. The optimal demand of x and y are such that:
px  x*
 I
(1   )  I
if   1    x* 
 x* 

px
p x  (   )
I
p y  y*

 y* 
 I
p y  (   )
if   1  

y* 
 I
py
I
If you use this information you do not have to perform any mathematical calculation to come
up with the right answers.
Svar:
A. C1 
C2
N2
 w  R1  w  N 1 
1 r
1 r
B.
4 points
4.A Show graphically and explain how economic inequality is measured.
4B. Describe 3 theories why economic inequality may affect the growth rate of GDP per
capita, at least during the transition to steady state.