The basic macro model
• In this lecture, we will cover the fundamental
macro model (also known as the IS-LM model).
• Developed in the 1950s/60s, economists at the
time believed that through this model they had
“solved” macroeconomics.
• This model was the basis of government policy
in Australia, the US and the UK up to the mid
1970s, when facts showed that macroeconomic
problems were not a thing of the past.
The goods market
• Our accounting identity from Macro 120
says that demand for goods and services:
Z ≡ C + I + G + (X – IM)
– Normally we just use “goods” as short-hand
for “goods and services”.
– Where C is private consumption of
households and firms, I is investment by
households and firms, G is government
consumption of goods and services, X is
exports and IM is imports.
Deriving the IS equation
• Assume we are in a “closed” economy (that
does not trade with the outside world), so X = IM
= 0. we will deal with open economies in a later
lecture.
• Assume consumption is a function of disposable
income so C(Y – T).
• Equilibrium in the goods market requires goods
demand, Z, is equal to goods supply, Y.
Y = C(Y – T) + I + G
• Is called the IS equation.
Linearizing consumption
• If we “linearize” consumption, we assume
consumption to be given by:
C = c0 + c1 (Y – T)
• Where c1 is our marginal propensity to
consume (MPC).
• We assume 0 < c1 < 1.
• Our IS equation becomes:
Y = c0 + c1 Y – c 1 T + I + G
The multiplier
• Rearranging we get:
1
Y
(c 0  c1T  I  G )
(1  c1 )
• Where our equilibrium level of Y will be a
function of parameters (c0 and c1) and our
exogenous variables (I, G and T).
• Equilibrium Y is increasing in c0 and c1 (for
sensible ranges).
1
• Equilibrium Y increases by (1  c ) for a change in I
and G and by(1cc ) for a change in T.
1
1
1
Equilibrium in the goods market
1
value(1  c1 )
• The
is called the “multiplier”.
• Is there a role for the government in this model?
Yes, through manipulating G and T. Raise G
and lower T in a recession, while lower G and
raise T in a boom.
• If the government raises G in a recession, by
how much will output rise?
1
 1 as 0  c1  1
(1  c1 )
• Which is why we call it the multiplier.
Variant: Balanced budget multiplier
• The government above was free to set G and T
however it wished. What if the government had to
control the budget deficit, so that G = T at all times?
• If we put the G = T requirement into the IS equation,
we get the balanced budget multiplier:
1
Y
(c 0  c1G  I  G )
(1  c1 )
1
Y
(c 0  I)  G
(1  c1 )
• So our new multiplier is 1.
Balanced budget multiplier
• Intuition: Why is the balanced budget multiplier
less than the multiplier without balancing the
budget?
• Answer: In the balanced budget case, the
government has to raise T by $1 when it raises
G by $1. Raising T will lower output but by less
than G raises output. The net result is a higher
level of output, but less than if the government
did not have to simultaneously raise taxes.
Investment
• The goods market model assumed that investment was
exogenous- that changes in Y did not impact investment.
• Assume investment is a function of production and
interest rates:
I = I(Y, i)
• We assume that investment and production are
positively-related and that investment and interest rates
are negatively-related.
• Intuition: As interest rates rise, the cost of capital to firms
rises, so fewer new projects are profitable.
New IS equation
• Our new IS equation is:
Y = C(Y-T) + I(Y, i) + G
• Since C(.) and I(.) are functions, G and T are the
only exogenous variables.
• The new IS equation represents the equilibrium
combinations of (Y, i) given the values of (G, T).
• Since we have two variables (Y, i) but only one
equation to determine them, the new IS equation
expresses a relationship between Y and i.
Linearizing investment
• Assume investment is linear in Y and i:
I  b 0  b1Y  b 2i
• Plugging this into the IS equation we get:
Y  c 0  c1 (Y  T)  b 0  b1Y  b 2i  G
1
Y
(c 0  c1T  b 0  b 2i  G)
(1  c1  b1 )
• Can we talk about a new multiplier?
New IS equation
• Answer: Not yet! As if we changed G, we will affect Y
and also i.
• What we have is a relationship between the equilibrium
values of (Y, i) and the exogenous variables (G, T).
• How are the equilibrium values of Y and I related?
Y
 b2

i (1  c1  b1 )
• As long as c1 + b1 < 1, we have Y negatively-related to i.
So if we graphed the IS curve, it would be down-wardsloping.
We need another equation!
• The new IS curve shows us possible
equilibrium values of (Y, i), but it does not
determine a unique value. There are an
infinite number of solutions for one
equation and two variables.
• We need another equation to have a
solvable problem: two equations, two
variables.
The money market
• Demand for money (Md) is increasing in the
money value of output and decreasing in the
interest rate.
• Intuition: If the economy produces more goods,
the economy will require more money to
exchange for those goods. Interest rates are the
time opportunity cost of holding money. If an
individual were not holding cash, that wealth
would be accumulating value in a bank or
investment at the rate of interest.
Demand for money
Md = L(Y, i)
• Assume that doubling output, doubles the
demand for money for any interest rate,
then this equation becomes:
Md = Y L(i)
• We have assumed that L(i) is decreasing
in i as above.
• Money supply (Ms) is exogenous and is
determined by the government.
Equilibrium in the money market
• Equilibrium in the money market requires that
money supply is equal to money demand.
Ms = Y L(i)
• This is called the “LM” equation. The
exogenous variable is Ms and the endogenous
variables are (Y, i). This is another relationship
in (Y, i).
s
Y  L' (i) M

2
i
(L(i) )
• So the LM curve is upward-sloping in (Y, i).
Combining the IS and LM
equations
• IS: Y = C(Y – T) + I + G
• LM: Ms = Y L(i)
• We have two equations in two variables (Y, i),
and so this equation is (generally) solvable for a
unique solution (Y*, i*) that satisfies both
equations.
• Only one set of values (Y*, i*) will simultaneously
solve both the IS and LM equations. So only
one set of values will lead to equilibrium in both
the goods and money markets.
Role of the government?
• Combining the IS and LM equations
means that we have two variables which
are jointly determined by the three
exogenous variables (Ms, G, T).
• We call policies involving Ms “monetary
policy” and policies involving G and T
“fiscal policy”.
• This was the dominant macro model of the
1950s and 1960s.
The IS-LM framework
• Fiscal policy (G, T) shifts the IS curve, while monetary
policy shifts the LM curve.
• An increase in G shifts IS to the right.
• An increase in T shifts IS to the left.
LM(Ms)
i
i*
IS(G,T)
Y*
Y
• An increase in Ms shifts LM to the right.
Experiments with IS-LM
• Show what happens in the IS-LM graph if
you
– Increase G or T or Ms
– Have a reduction in C or I
– Have a decrease in Md
• For Thursday: Do Problem 4 and 5 in
Chapter 5.