Seminar assignment week 18
Written by Jørgen and Marit
Problem 1
Two period dynamic model where utility of the representative consumer is given by
1
U    x1 (q ) dq 
 0



1
    x2 (q ) dq 
 0



where q is the different goods, x i is the amount of good q consumed in period i and  is the
subjective discount factor. The consumer is endowed with L units of labor each period which he
supplies inelastically. The consumer owns all profits. Wage is set equal to 1.
The good q is produced by a competitive fringe using a CRS technology, converting one unit of labor
into one unit of the good. In addition there is a potential monopolist in each q sector who can invest F
units of labor in the first period and then produce  >1 of output per units of labor in the second
period.
Interpretation of  :
The intertemporal elasticity of substitution is given by 1 1   . This implies that  gives us
information of the consumer’s willingness to substitute consumption across periods. The higher the 
the less averse the consumer is to substitute consumption across periods. When  =1 the consumer is
indifferent about when to consume his income.
Interpretation of 
The elasticity of substitution between different goods in the same period is given by
1
.
1 
Derivation of equation (18):
The representative consumer can either consume all his wages L in the first period or save part of his
wages at an interest rate r. In order for the investment to take place, the consumer must be willing to
accept a lower level of consumption today in order to consume more tomorrow.
Budget constraints:
c1  s  y1
c2  (1  r ) s  y2
where c1 , y1 is consumption and income today while c2 , y2 is consumption and income in the
next period.
Solve for the intertemporal budget constraint:
(1  r )c1  c2  (1  r ) y1  y2
The consumer problem consists of
max
u(c1 )  u(c2 ) st (1  r)c1  c2  (1  r) y1  y2
Solve the budget constraint for c2 and substitute into the utility function
max
u(c1 )  u( y2  (1  r ) y1  (1  r )c1 )
FOC:
max
u (c1 )  u( y2  (1  r ) y1  (1  r )c1 )
u ' (c1 )   (1  r )u ' (c2 )  0
(*)  * 
1
 u ' ( c2 )

1 r
u ' (c1 )
In equilibrium the discount factor must be equal to the inverse of the return on savings. The consumer
and the market must have the same valuation of the future.
Further, I choose to simplify by only looking at one good. The utility function now becomes

U  c1  c2

dU
 1
 c1
dc1

dU
 1
 c2
dc2
Insert into (*)
* 
c2 1
 1
c1
Equation 18 is found by plugging in the incomes of period 1 and period 2 in the case of
industrilization:
 1
 L 
18)  *   

LF 
Thus the interest rate is adjusted in equilibrium in order to induce savings and prevent consumption
smoothing. The higher the value of  the lower the interest rate must be in order for the consumer to
shift his consumption from period 1 to period 2.
The present value of the profit of the potential monopolist is given by
   * ay2  F , where a  1  (1  ) is the marginal profit rate. In the first period the potential
monopolist is acting as a competitive actor, thus profits are zero but he incurs the fixed cost F. Given
the interest rate given by (18), the present value of profits must be positive in order for the potential
monopolist to take on the investment:
 1
 L 
(19)   (aL)  

 LF 
F 0
The reason why we get multiple equilibria in this model is that the profits of the firms do not take into
account the positive effect on aggregate demand that the investment induces. Even if an individual
firm looses money by investing, it still lowers the demand in the first period and raises it in the second
period. Raising demand in the second period makes investments more profitable for other firms as
well. This shift in income makes the big push possible. For the same parameter values, we may have
two different equilibria. If firms expect that other firms will industrialize then they will also
industrialize. If the firm expect that no other firm will industrialize then they will not industrialize.
Problem 2
a.
Rent is defined as the return to an asset in excess of its best alternative earning.
Rent seeking can be defined as the pursuit of rents. The activity persons of firms engage in to
be allocated rights that later entitle them to receive rents.
One example of rent is the value of land where there is a difference between the values of its
alternative uses, such as if it contains oil, and has an alternative use as farmland. The rent is
then the value of the land as an oil field minus its value as farmland. A different example is a
legal import licence for a particular good or a patent right. This right allow the owner of the
licence to have a monopoly of a particular good, which can be used to collect profit that
would not be collectable in a competitive setting.
Rent seeking might be very different activities including schooling and bribing. Schooling can
be a rent seeking activity when the level of schooling needed to get the job exceeds the level
schooling needed to do the job. A well known example is when persons take a college (or
university) degree, not to learn the skills for a job, but to get the job. Bribing can be paying a
government official to give you a particular licence which you later can use for your own
gain, or the design of the bureaucracy so that such bribes come natural with issuing the
licence.
b.
The “tollbooth” theory of rent seeking is a theory that explains large and inefficient
bureaucracy with stating that such bureaucracy is in place to allow government officials to
collect rent and bribes. (Rent and bribes can be the same thing, but “speed money” need not
be rent. And rent does not need to be corruption.)
Other explanations for large and inefficient bureaucracy can be1; relative low level of
schooling, unemployment, the form, function and ideology of the state. In some positions
quality can be substituted with quantity. In Egypt there was2 a law giving a state job to anyone
holding a college degree. With a state structured around central planning and authority more
administration might be needed, in combination with a shortage of infrastructure this might
result in a large and inefficient bureaucracy.
c.
The discovery of a natural resource in a country may increase rent-seeking activities since the
amount of rent possible has increased. More rent means that the possible reward for rent
seeking increases. Thus can more resources (rationally) be devoted to getting the necessary
licences, contracts, positions etc. to collect rent from the extraction of the natural resource.
A result from this is that the discovery of a natural resource need not be in the benefit of the
broader public. It might very well be that more people loose out, as already scarce resources is
1
This is not facts but me thinking of possibilities.
To my knowledge it might still be in place, or never have existed, but the law was referred to by Todaro in his
development economy textbook used in the 1910 course.
2
used for rent seeking and not used for investment in other sectors where the money is used to
produce not extract.3
I think that the countries most hurt by rent seeking are the countries that lack the necessary
institutions to prevent rent seeking. That means poor, less developed countries and countries
with totalitarian regimes. Relatively rich, and more democratic countries (with more
developed control mechanisms) I would expect to do better, but it is very hard to imagine a
country where no rent seeking is taking place.
Problem 3
Rodrik’s model of policy uncertainty
Rodrik considers an economy where there has just been introduced a policy reform. Before the policy
reform the return from investment was given by r  t0 , while afterwards it was given by r  t , where
t< t 0 .Policy uncertainty is measured by a probability  , the likelihood of policy reversal. A policy
reversal means going back to the state before the reform, i.e. the return from capital is then back to
r  t0 .
Now let’s consider the investment decision of a risk neutral agent. He can either move his capital
where the capital earns r  t or he can leave the investment at the same place earning r*. The value
of the second option can then be denoted as
1) V0 
r*

, where  is the investor’s discount factor.
The value of reallocating capital V1 depends on t and the probability of policy reversal:


2) V1  r  t   (V1  V1R ) / 
Where V1R is the value of the investment when the policy is reversed. The value of the investing in
this country now have two different components: r  t is the value of steady flow of benefits and
 (V1  V1R ) is the expected capital loss.
V1R can be determined as follows: If the policy is reversed the investor has a choice of either moving
his capital back or leaving it put. Assume that there are exit costs when pulling out the investment
equal to  . The investor will move the capital if r*-  > r  t0 .
V1R is then given by
3
Mehlum has discussed this question.
(r  t 0 ) /  _ if _ t  t 0  small
3) V1R  
(r * /  )   _ if _ t  t 0  l arg e
V1 is given by
4) V1  (    ) 1 (r  t )   max (r  t0 ) /  , (r * /  )   
Now, we can pose the question, what will it take for the investor to move his capital when the
reform is implemented? The investor will only choose to do so if the net benefits of
reallocating is positive. Denoting  as the entry costs, the condition for reallocating capital is
given by
5) V1  V0  
Assuming that the policy reversal is large ( t  t0 large), substituting in from 1) and 4)
(r  t )  r*     (   )
This equation links the investor’s response to the size of the policy reform, the probability of
policy reversal and the size of entry/exit costs. The net benefit of reallocating capital after the
reform must be significantly high enough to cover the one time cost of entering  (the flow
equivalent of the entry cost) and the likelihood of policy reversal (  (   ) ).
Higher probability of reversal means that the perceived profits of reallocating capital goes
down. The investor will require a high compensation in the form of a low (or even negative t)
in order to invest.
a) A reversal can be re-reversed so that we can get the good policy back after a while.
This changes the present value of future losses. If the policy is re-reversed with a
probability  , then 2) becomes


V  r  t   ((1   )(V  V )/ 
2*) V1  r  t   (V1  V1R   (V1  V1R ) / 
1
1
R
1
2*) implies that the present value of future profits gets higher when there is a possibility of rereversal. Thus, given that  is exogenous it will be easier to attract capital.
b) A policy reversal may only be partial, so we can end up in a situation where the policy
is neither as good as the good case but not as bad as the bad case.
This has the impact of increasing the value of profits when the policy is reversed
compared to when the reversal leads back to the status quo.
V1Rnew  V1R .
If we insert the new value of profits into 2) we see that this has the effect of increasing the
present value of profits when reallocating capital. The loss of policy reversal has
decreased, thus it is now easier to attract capital.