ECONOMICS 4012
Problem Set 3: DAD alone
This is due at class time on Monday, October 24.
Below you find values of the parameters:  and , and Yn and Y0. All other initial values of
variables are zero unless otherwise specified.
= 1.25
 = 1000
Yn=1500
Y0 = 1500
For each case below, you are to find values for output (Yt ) and inflation () for three time
periods: t=1,3. Since we’re interested in inflation/output dynamics, in each case you begin with
full employment. The Aggregate Supply curve here is perfectly horizontal at  = 0, and
perfectly vertical at Yn; it is the MAS(NK).
In each case you use equation (I. vi) from the notes: Yt = Yt-1 + at + (mt – t ), to introduce a
change, and to find the time paths of inflation and output for the first three periods after the initial
period, ie for t=1,3. You do each case several times, one for each of two different monetary
policies: no “accommocation” and “lagged accommodation”.
You always start with Y0 = Yn = 1500. Values for m0 and  are given. You have already spent
much time, in Economics 1012 and 3012, looking at situations where the policy variables
decrease. These situations are just the same as having IS and LM alone: Prices, P, are fixed; 
= 0, you get values of Y1 that are less than Yn, and those values of Y1 are in dynamic
equlibrium, Ye. It’s all over. So here I have you deal only with situations in which something
increases: either 1 > 0 exogenously (supply shock); or a1 or m1 > 0.
To use equation (I. vi) with a supply shock, just substitute the value of 1 into the equation and
solve for Y1. Then proceed.
To use equation (I. vi) for expansionary policy follow the algorithm below:
1) Values for a1 and m1 are given. Temporarily assume 1 = 0 and solve for Y1. Call this
temporary value of Y1 , Yˆ1 . Yˆ1 will be greater than Yn, so cannot be the value of Y1.
2)
SoY1 = Yn. Substitute the value of Yn for Y1 in equation (I. vi) and, with the given values of
a1 and m1, solve for 1.
3) If there is no accommodation, you are finished. If there is lagged accommodation, put in
new value of m2 , m2 = 1 , and repeat steps 1 and 2. And repeat until you finish t = 3.
You now have Yt and t for t = 1,3. In each case draw crude graphs in the  , Y space, showing
movements along and/or shifts in the DAD curve during the three periods, and label the
relevant points with numbers on each axis. Unless otherwise noted, each case begins with no
inflation, 0 = 0, and full employment, Y0 = Yn. NOTE: inflation rates are given as decimals:
10% inflation is t = .10.
1. A supply shock with no accommodation; m0 = 0 = 0; 1 = .10; mt = 0 for all t. Note: t = 0
is the default. Unless there is pressure on  from something it returns to zero.
a. There are no other changes. Find Yt and t for t = 1,3.
b. Reacting to the unemployment, government increases spending or cuts taxes, setting a2
= 80. The change is permanent, so a3 = 0. Find Yt and t for t = 2,3.
2. A supply shock with lagged accommodation; m0 = 0 = 0; 1 = .10;
mt = t-1 for t = 2,3. There are no other changes. Find Yt and t for t = 2,3.
3. m0 = 0 = 0. Expansionary fiscal policy: the government, believing that it can reduce
unemployment, sets a1 = 40.
a. The change is permanent, so a2 and a3 = 0. mt = 0 for all t. Find Yt and t for t = 1,3.
b. The government, still convinced that it can reduce unemployment, orders lagged
accommodation from the Bank of Canada. So mt = t-1 for t = 2,3. Find Yt and t for t =
2,3.
4. m0 = 0 = 0. Expansionary monetary policy: the government, believing that it can reduce
unemployment, instructs the Bank of Canada to set m1 = .08.
a. mt = 0 for t = 2,3. Find Yt and t for t = 1,3.
b. The government, still convinced that it can reduce unemployment, orders lagged
accommodation from the Bank of Canada. So mt = t-1 for t = 2,3. Find Yt and t for t =
2,3.
5. Begin with inflationary equilibrium: m0 = 0 = .125.
a. Government, worried about inflation, cuts spending, setting a1 = – 100. The change is
permanent, so a2 and a3 = 0. mt = t-1 for all t. Find Yt and t for t = 1,3.
b. Government, worried about inflation, instructs the B of C to stop accommodating. The
BofC sets mt = 0 for t = 1,3. Find Yt and t for t = 1,3