Columbia College. Economics 3213
Professor Xavier Presents...
Problem Set 6
(1) The King of Fools
Consider the
classical model we saw in class. Imagine that the supply depends positively on the
interest rate, while consumption demand depends negatively. Imagine that the economy is in
a position of equilibrium.
(I) Consider a temporary
increase in the level of technology (that is A1 increases but A2
and all future As remain the same). This temporary increase could represent good weather
(which affects today's supply but not tomorrow's). How will the equilibrium c, y and r in
period 1 
change?
(II) Consider now a permanent
increase in the level of technology (A1, A2, A3, etc all
increase in the same proportion). This permanent increase in A could be the result of a
technological improvement. How will the equilibrium c, y and r in period 1 change? Is your
answer different from (I)? If so, why?
(III) Consider
finally an anticipated increase in A. That is, imagine that while A1
does not increase, we KNOW that A2 and all future As will increase (some better
technology has been discovered, but it will not be implemented until next year). How will
the equilibrium c, y and r in period 1 change? If anything happened to current levels of
c, y and r, explain why?
(2) Esmeralda
Define each of the following terms:
(A) Price Level 
(B) Nominal Interest Rate
(C) Real Interest Rate
(D) Nominal GDP
(E) Real Consumption
(F) Inflation Rate
(G) Money
(3) Frollo
Imagine that the
nominal interest rate between year 1 and year 2 was 5 percent (that is, R=0.05). Imagine
also that the inflation rate was 5 percent (
=0.05).
(A) What is the EXACT relation between the NOMINAL
interest rate and the REAL interest rate? (Make sure you DERIVE this result).
(B) If R=0.05 and =0.05, what is the EXACT VALUE of
the REAL interest rate, r?
(C) If r and are small, we can usually neglect
the product r times and use an
approximate formula. What is the APPROXIMATE relation between R and r now? Why? Using
R=0.05 and =0.05, what is the
approximate value for r? Is this different from the value you get in (II.B)? Why or why
not?
(D) Suppose now that
the nominal interest rate is R=0.05 and the inflation rate is =0.02 (2 percent). Compute the EXACT value and
the APPROXIMATE value for the real interest rate, r. Are they the same now? How big is the
"mistake" we would 
make if we use the approximate formula instead of the exact
formula? Why?
(E) Some countries
have large inflation and interest rates. Consider now a country with an inflation rate of
100 percent (=1.00) and a
nominal interest rate of 110 percent (R=1.100) What would be the EXACT value of the real
interest rate in this case? What would be the computed real interest rate if, instead, we
use the APPROXIMATE formula? How big is the mistake now? Do you think that the
approximation can be used in high inflation countries?
(4) Phoebus
Does Real Consumption depend on Nominal or Real interest rates? Why? Does labor supply depend on nominal or real interest rates? Why?
Come one, come all
Leave your looms and milking stools
Coop the hens and pen the mules
Come one, come all
Close the churches and the schools
It's the day for breaking rules
Come and join the feast of...
Fools!
Once a year we throw a party here in town
Once a year we turn all Paris upside down
Ev'ry man's a king and ev'ry king's a clown
Once again it's Topsy Turvy Day
Good is bad and best is worst and west is east
On the day we think the most of those with least
Ev'rything is topsy turvy at the feast of fools!
Topsy turvy
Everything is upsy-daisy
Topsy turvy
Ev'ryone is acting crazy
Dross is gold and weeds are a bouquet
That's the way on Topsy Turvy Day