Quantitative Intermediate Economics
Final exam: sample solutions
Winter 2016
1. Since the two firms are producing an identical product, the price
charged will be identical: PA (Q ) = PB (Q ) = P (Q ) = 150 2Q ,
+ q .
where Q = qA
B
(a) No sunk costs. Eac

would also be zero. This is not surprising since the fundamental
assumption of the OLG theory is that fiat money possesses a onedimensional use, i.e. it is a store-of-value function for carrying
purchasing power to the future a use that is totally elimina

price ratio and the real rate of return remain the same in the two cases.
22.1.2 Inefficiency of monetary expansion with seigniorage as a taxation
device Remember that in the case being analyzed in this section the
government is assumed to destroy commodi

monetary expansion. 738 Overlapping generations models Welfare loss
from changes in the velocity of circulation An alternative to monetary
expansion is increases in the velocity of circulation of money. Velocity is
constant at unity in this model, so that

including the domestic one, simultaneously will only arise because of
legal and other restrictions on the use of foreign currencies. In the real
world, national currencies usually remain the most commonly used fiat
money in their own nation, even though t

real balances is given by the part of real saving that the individual wants
to carry forward in the form of real balances. Let the per capita demand
for and supply of nominal balances after the open market operations be
designated respectively by md t and

initial old would also benefit from moving from any point on AW o to
AW o, since they would receive a higher level of consumption.
Therefore, both the young and the old suffer a welfare loss because of
the divergence between the personal budget line and t

faith (or expectation) is firmly held that no future generation will make
the fiat money inconvertible into commodities directly or indirectly by
the substitution of a new currency which renders the preceding one
inconvertible into the new one. Further, t

model. In the OLG models, the actual bubble on the value of fiat money
has consequences for the consumption and saving path over time.
Sunspots and bubbles are defined relative to the outcomes based on
market fundamentals, which are defined in the OLG lit

Chapter 24 on monetary growth theory. Conclusions The OLG
framework offers an alternative format to MIUF and MIPF theories (in
which economic agents have an infinite horizon) for modeling the
demand for money. They are especially appealing to those who be

+bo t] (23) Hence: pt = (Mt +Bt)/[Nt(wy t cy t)] (24) Since cy t on the
right-hand side of (24) depends on pt+1/pt, we have: pt = (Mt +Bt)/
[Nt(wy t cy t(pt+1/pt,wy t,wo t+1)] (24 ) Hence, the current price level
depends on the intertemporal price ratio p

asset, both of which are simultaneously held by the public and can also
be held by the government. This theorem states that open market
operations between money and another asset, with government
consumption held constant, will not have any real effects (

are often less than 2 percent of GDP but could be as high as 10 percent
or more, depending on the extent of money creation and inflation; as a
percentage of government expenditures, the estimates are less than 10
percent for most countries, but much highe

+dmt)+pt+1t(kt dkt)+pt+1(t pt/pt+1)dkg t (28) where kg t are the
per capita government stocks of the stored commodity, with a gross
return of kg t. In (27), the young carry forward (mt + dmt) of money and
(kt dkt) of the stored commodity. In (28), the old

price decrease under a constant money supply. The basic OLG model
does poorly in generating implications consistent with the stylized
empirical facts about money in the economy. Review and discussion
questions 1. Specify and discuss at least five stylized

exist any legal barriers to the use of US currency relative to Canadian
one. Both circulate freely, payments at many stores can be made in
either currency, deposits in banks can be held in either currency, etc.,
and, between 1980 and 2003, the expectation

> 1, so that the monetary expansion increases the private rate of
exchange above the social rate and makes the individual choose too little
of old-age consumption and too much of consumption when young. It
does this by depreciating the value of money hold

commodity by the representative private firm, with full employment in
the economy. Assume that each worker produces one unit of the
commodity (without requiring physical capital). Specifying any other
assumptions that you need to make, derive the implicat

a close relationship between the demand for money and saving, rather
than between the demand for money and current consumption
expenditures. OLG models imply multiple equilibria for the price
level and the return on money but only two stationary equilibri

money demand comes from the young. Further, mdyt = sy t. Hence,
money demand is determined only by the saving of the young. In the
case of price stability, i.e. with = n, we get: co t+1 = c y t (55) md t/pt
= wy t c y t = wy t [1/(1+)]Wt (56) Hence, the d

there was no net seigniorage accruing to the government from money
creation. Seigniorage is the revenue from monetary expansion.1 The
nominal value of the seigniorage per young person from monetary
expansion at the gross rate in period t is given by: Gt =

The OLG model: seigniorage 751 Figure 21.2 of Chapter 21, any point
on this segment is inferior in utility to some points on the segment XW o
of the economys constraint, with the latter offering more of both cy and
co. Since the segment XW o is available

this chapter, expectations do play such a role with respect to the value of
fiat money in the OLG models, so that these models are very prone to
sunspot activity. The common limitation of the analysis of such models
to stationary equilibrium states is a m

population growth Given a population growth rate of n, price stability
could be achieved by a money supply rule that sets equal to n. With
such a rule, prices would be stable but the monetary expansion would
still impose an allocative inefficiency and a w

open market operations, which maintain the sum of money and bonds
but vary their proportion, are efficient. Distinctive roles of money and
bonds in real-world economies The modern economy has distinct roles
for money (whether fiat money or deposits in ban

10 countries above even this level. On average, seigniorage was about
2.5 percent of GDP and financed about 10 percent of government
spending. 22.2 Fiat money and bonds in the OLG framework Fiat money
in the preceding OLG models functions merely as a stor

since he would either consume all his endowments or convert any saving
into money m for possible use in the future. 18 Since the individual
derives no utility from unspent money balances or unconsumed
commodities left over at the end of t +1, utility maxi

= wy +(/n)wo (16) W o = (n/)[wy +(/n)wo] (16 ) Since the
seigniorage from monetary expansion is now no longer returned to the
people, the personal budget line from (15) lies inside the one (not shown
in Figure 22.1) from equation (21.43), so that welfare

Discuss in the context of the OLG model the validity of Friedmans
money supply rule: the best monetary policy is one that increases the
money supply at a steady low rate. 12. Given the stylized empirical facts
about money in the economy, discuss the valid

with B offering greater utility than A. Since the segment AW o offers
socially feasible consumption opportunities not available for > 1, the
individual would have a higher level of utility for = 1 than for > 1.
The individual is therefore worse off with m

o and the economys per capita constraint W yW o, the former has a
flatter slope equal to (n/), for n, > 1, than the latter whose slope from
(3) equals (n). Let the intersection point between these lines be at X.
Similar to our arguments in Chapter 21 for

amount of total saving 13 After compensation for the riskiness of the
return on the stored commodity, the gross return on the stored
commodity will equal pt/pt+1, which is the gross return on the riskless
asset money. 758 Overlapping generations models by

indirectly include money holdings as an argument, thereby meeting the
requirement of the benchmark OLG models of fiat money that money is
intrinsically useless. The appropriate lifetime budget constraint for the
case of population growth at the rate n and

are: ptcy t +mt = ptwy t (11) pt+1co t+1 = pt+1wo t+1 +mt (12)5 5 Note
the difference between (12) and equation (21.40) of Chapter 21, though
both involve an identical monetary expansion. 750 Overlapping
generations models Substituting (11) in (12) to eli

for co whereas the present money supply rule with = n makes it 1.
We leave it to the reader to show that a negative population growth rate
with n < 1 (the declining population case) but a stable money supply will
cause inflation but not impose a welfare l