Econ 206

Prof. Franc Ortega

Question 1: The IS-LM model and the government-spending multiplier

Consider an economy with the following data:

C(Y-T) = 125 + 0.75(Y-T)

Please note that consumption does not depend on the interest rate but investment does.
Note also that the initial price level and government purchases are some constant P and
G, respectively. Exports are equal to imports. Assume that the full-employment level of
output equals 1,600.

a) Construct the IS curve. Express r as a function of Y. What is the slope dr/dY?

For the IS curve, we use the market clearing condition for the goods market (or for the
loans and credit market):
Y = C(Y – T) + I(r) + G
Y = 1000 + 4G – 40r
r = 25 + (G/10) –(Y/40).

The slope is the derivative with respect to Y and will equal –(1/40). It is negative
because the IS slopes downward.

b) Construct the LM curve. Express r as a function of Y. What is the slope dr/dY?

For the LM curve, we use the market clearing condition for real money balances:
M/P = L(Y, r),
800/P = 0.8Y – 16r,
r = (Y/20) – (50/P).

The slope is the derivative with respect to Y and will be (1/20). It is positive because the
LM slopes upward.

c) Calculate the short-run equilibrium for this economy and graph it (using the IS
and LM curves). Suppose G=150 and P=1.

We simply need to solve the following system of equations:

r = 25 + (150/10) –(Y/40).

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 r = (Y/20) – (50/1).

The solution is Y*=1200 and r*=10. At these values for income and the interest rate,
investment and consumption equal I*=100 and C*=950.

Graphically, this is the point where the IS and LM curves intersect.

d) Suppose that government purchases increase to 250. Find the new short-run
equilibrium (that is, P=1 still) both graphically and numerically. What is the
increase in real GDP? What is the change in consumption and in investment?

We simply need to solve the following system of equations:

r = 25 + (250/10) –(Y/40).
r = (Y/20) – (50/1).

The solution is Y*=1333.3 and r*=16.7. At these values for income and the interest rate,
investment and consumption equal I*=33.3 and C*=1050.

Thus investment has fallen by 66.7 units and consumption has increased by 100 units,
that is, an increase in private sector spending (C+I) equal to 33.3 units. In this example
consumption is solely a function of disposable income and, hence, it increases in the
short run.

Overall income has increased by 133.3 units as a result of the increase in government
purchases equal to 100. Intuitively, the increase in the demand for goods by the
government increases income. As income rises, consumption also rises, increasing the
demand for goods even further. As a result real GDP rises by more than the increase
in government purchases. This is known as the multiplier effect of government
purchases.

e) Find also the long-run equilibrium (when G=250), given that the full-
employment level of output is equal to 1600. Report the levels of real GDP, interest
rate, price level, consumption and investment. Show it also graphically.

Let us proceed in the usual three steps. First step. In the long-run equilibrium, income
and output will be given by their full-employment levels i.e. Y = 1600.

Second step. We can now use the IS and the full-employment level of output to find the
long-run real interest rate:

IS: r = 25 + (G/10) –(Y/40).

Third step. We can now use the LM, full-employment income and the long-run interest
rate to find the price level.

LM: r = (Y/20) – (50/P).

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Solving the equation we obtain P=0.71. Graphically, since the short-run equilibrium has
a level of income below full employment, the LM will need to shift to the right. That
is, the price level will have to fall (deflation).

Long-run levels of consumption and investment are C*=1250 and I*=100.

Question 2
Consider the policy measures below. For each of these measures say how do they shift
the IS or the LM and what the short-run economic effects of each measure should be
based on the IS-LM model.

a) The Fed should buy more debt in open market operations.

When the Fed buys debt it pays with new money. This increases the money supply,
which shifts the LM curve to the right. As a result, income rises and the real interest rate
falls in the short-run.

b) The Fed should announce and pursue generating some inflation. As a result the
return to firms from hoarding cash will be negative and they may instead turn
those resources into investment.

This increase in investment can be interpreted as an increase in the intercept of the

This is like an increase in investor’s confidence. Thus it shifts the IS curve to the right.
In the short run income and the real interest rate will both rise.

c) The Administration should put more pressure on China to appreciate its

When the Chinese currency appreciates relative to the USD, we expect US exports to
China to increase and US imports from China to fall. This is an increase in net exports,
which shifts the IS curve to the right. Thus in the short run both income and the real
interest rate will rise.

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Question 3: Economic outlook.
Read the November 2011 economic outlook by the Kansas City Fed.

A. In the period between 2004 and nowadays, when did actual real GDP start
falling below its long-run value? At which point did the gap between actual and
potential output stop growing?

ANS: Real GDP began to fall after 2008. Real GDP began to rise again,
closing the growth of the gap between estimated and actual GDP, during 2009.

B. Given that in the long run actual output is always close to its potential value,
what is your forecast regarding real GDP growth for the next few years? Is real GDP
going to grow more than in the last couple of years or less? According to the forecasts
in the outlook, what are the forecasted growth rates of real GDP for years 2012, 2013
and 2014? How about beyond?

ANS: According to the graphs regarding real GDP growth, the next couple
of years, 2011 to 2014, will provide a higher growth rate than the last couple of
years, but none above 2010s GDP growth rate of about 3.2%. The forecasted
growth rates for 2012 to 2014 are about 2.25%, 2.75%, and 2.85% respectively.
Beyond 2014, the growth rate of real GDP is forecasted to be between 2.25% and
3%.

C. According to the forecasts in the outlook, what are the forecasted inflation
rates for years 2011, 2012 and 2013? And beyond?

ANS: The forecasted inflation rates for years 2011 to 2013 are
approximately 3.25%, 2%, and 2% respectively. Beyond that it is expected to be
between 1.5% and 2%.