Short Run
Closed-economy IS-LM model, which focuses only on the relationship between the interest rate and output. Assume price is fixed.
Equilibrium Output
The 45 degree line means production and income are equal. The demand curve is
ZZ = C + I + G = c0 + c1(Y-T) + I + G = c0 -c1T + I + G +c1Y
ZZ = autonomous spending + c1Y
autonomous spending is the intercept with vertical axis
c1 is the propensity to consume
Equilibrium happens when demand = production.
Goods Market
Y = C + I + G and S = Y - T - C = I + G - T
so S + T = I + G
if G = T => S = I
Financial Market
demand for money, depends on income and interest rate
Md = $Y L(i) $Y+ , L(i)-
A rise in income leads to rise in demand for money
A rise in interest leads to decrease in demand for money
intersection of money supply and money demand is equilibrium interest rate.
real money supply = real money demand
Ms/P = Y L(i)
CB control currency and reserves
high powered money (monetary base) = currency + reserves
Let CU be currency, D demand deposit, M money supply, c is proportion of money in currency, H is monetary base,
θ is reserve ratio
M = CU + D ; CU = cM ; D = (1-c)M ; R =
θD
H = CU + R
M = (1/(c +
θ(1-c))) H
Q: Can CB closely control the money supply?
Ans: No, CB control H and
θ, but cannot control c, so CB cannot closely control money supply
zero lower bound: nominal interest rate cannot go below zero
liquidity trap: when nominal interest rate is zero, monetary policy cannot lower it further, implying monetary policy is not effective
Goods Market in open economy
ZZ: demand for domestic goods
AA: domestic demand for domestic goods
DD: domestic demand for goods
As income goes up, some additional domestic demand falls on imports. So AA is flatter than DD. Exports do not depend on domestic income, AA and ZZ have some slope.
As income (output) goes up, imports increase, exports do not change. So NX decrease.
Medium Run
Medium run: 1) price can change 2) include labor market
Labor market:
Wage setting: W = PeF(u,z) ; z: catchall variable for all other variables
Price setting P = (1 + m) W ; m: mark-up of price over wage
equilibrium in labor market: F(u,z) = 1/(1+m)
Original Phillips Curve
π
e = π
- expected inflation is rather constant
_
π = π+ (m + z) - αu
t
So, negative relationship between unemployment and inflation.
Original phillips curve implies there is no natural rate of unemployment
Modified phillips curve
from P = (1 + m) PeF(u,z)
let F(u,z) = 1 - αu+ z ; α: strength of unemployment on wage
P = (1 + m) (1 - αu+ z)
so after maths transform:π
t - π
t-1 = (m + z) - αu
t
if 0 = (m + z) - αu
t and so the natural rate of unemployment is
u
n = (m + z) /α
Phillips curve and the natural rate of unemployment
π
t - π
t-1 = -α(u
t - (m + z)/α)
let u
n = (m + z)/α ; u
n : natural rate of unemployment
π
t - π
t-1 = - α(u
t - u
n )
Implications:
The natural rate of unemployment is the rate that keep inflation rate constant, or we call this rate NAIRU - non accelerating inflation rate of unemployment
Not sustainable to keep unemployment rate below u
n, because if you do that, inflation gonna rise
Short to Medium Run : The IS-LM-PC model
Modified phillips curve
π
t - π
t-1 = (m + z) - αu
t
π
t - π
t-1 = (α/L)(Y - Y
n ) ; L: labor force size
Y
n is potential output, so when output is above potential output, inflation rises
IS-LM in equilibrium in the short run, but output is above potential output, so inflation rises, or economy overheating
A rising inflationary pressure makes central bank raise the policy rate. The at medium run, Y and r are at natural levels and inflation rate may not change.
Zero lower bound:
Economy in recession, and output gap is negative (Y - Y
n < 0).
Central bank need to reduce real policy rate to restore Y to Y
n and make inflation stable. But, zero lower bound constraint make it impossible to achieve a negative real policy rate.
Central bank controls nominal rate only.
deflation and negative output gap feed on each other. Lower output leads to more deflation, more deflation lead to higher
real interest rate and lower output.
Long Run
Production function: Y = F (K,N)
assumed to be constant returns to scale, if K and N are doubled, output will also double.
Y/N = F(K/N, 1) K - capital, N - worker
If only one factor of production is doubled, the output less than double (decreasing returns to scale)
In the interactions between output and capital, there is a steady state, as shown by equation below
sf(K*/N) =
𝛿(K*/N) or s(Y*/N) =
𝛿(K*/N)
where s: saving ,
𝛿: depreciation
It is interpreted as, additional machines invested = machines that are depreciated.
If savings > depreciation, Yt/N will rise as depicted in diagram below.
The golden rule level of consumption is the saving rate that yields the highest level of consumption in steady state.
We have endogenous growth mode, where a steady growth is achieved
without technological progress. The model indicates that in the long run, growth rate depends on savings rate and rate of spending on education.
To include technological progress effect on rate of growth, let
Y = F(K, N, A) where A: tech, K: capital, N: labor
Y = F(K, AN) another form
Y/AN = F(K/AN, 1)
or Y/AN = f(K/AN) output per effective worker is a function of capital per effective worker
Let I = S = sY
I/AN = sY/AN
The g
A is growth rate of technology progress
The g
N is growth rate of workers
The above graph says output per effective worker (Y/AN) and capital per effective worker (K/AN) converge in the long run.
I =
𝛿K + (g
A + g
N)K = (
𝛿 +
gA +g
N)K
I/AN = (
𝛿 +
gA +g
N)K/AN
At steady state :
Y/AN, K/AN the LR growth is 0
Y/N, K/N the LR growth is g
A
Y, K the LR growth is g
A + g
N
Expectations
IS relationship
Y = C(Y-T) + I(Y, r+x) + G
A(Y, T, r, x) = C(Y-T) + I(Y, r+x) A:aggregate private spending
Y = A(Y, T, r, x) + G
adding expected values of future variables
Y = A(Y, T, r, Ye, Te, re) + G
The effects of expansionary monetary policy and expectation
Without expectation, monetary expansion would lead to a fall in policy rate from r to r" and output rises from Y
A to Y
B. WIth expectation, IS also shifts right and output rises from Y
A to Yc.
Budget deficit reduction
SR: A -> B, Y0->Y1 lower spending and lower output
MR: r↓ , Y1 -> Y0 due to lower interest rate, unchanged output, higher saving and higher
private investment (Because output unchanged, gov spending is reduced, so private investment is increased.)
LR: I↑(Y, r↓-x) higher investment leads to higher capital and higher output
Expected policy change will lead to future consumer response, but not present consumer response (false)
Exchange Rate
real FX rate = nominal FX rate (domestic Price / foreign Price)
ε = EP/P* ; E - nominal exchange rate, P - domestic price, P* - foreign price
if P < P* , meaning domestic goods is cheaper, therefore ε < E
In the short run, price level is fixed, a country with fixed exchange rate regime, cannot use monetary policy and cannot adjust exchange rate
In medium run, price can change, so a country can adjust its real exchange rate through price changes, instead of adjusting its nominal exchange rate.
Uncovered Interest rate parity
(1 + i) = (1 + i*) E / E*
the E* is expected future exchange rate
the i* is foreign interest rate
the i is domestic interest rate
Approximate formula
i = i* - ( E* - E ) / E
Real effective exchange rate (REER) : weighted average of a country's currency relative to an index or basket of other major currencies, adjusted for inflation
nominal exchange rate and real exchange rate, in SR, tend to move in the same direction, in middle run, will they move in the same direction? (uncertain)
IS-LM analysis
1) Use the IS-LM framework to determine SR equilibrium of tax cut. Explain its effect to Y, r, C, I, S
Ans: The effects of a cut in taxes, the IS curve shift to the right, Y increase, r does not change.
C ↑ as T goes down
S + T = I + G => I = S if T = G
2) Use the IS-LM-PC framework to evaluate a medium run equilibrium of tax cut. Explain its effect to Y, r, C, I, S
Ans: The effects of a cut in taxes, the IS curve shift to the right, Y increase, the change in inflation is positive. so inflation goes up. It is rising inflationary pressure. CB raise its policy rate, r ↑. Y goes back to original output. S is uncertain. I is uncertain. C will increase.
3) If tax cut partly involves reduction in import tariff for energy efficient machines such that many firms are now able to buy these machines and significantly reduce their energy costs. Use IS-LM-PC framework to evaluate the simultaneous effects (medium run equilibrium) of tax cut and reduction in energy cost on Y, r, C, I and S in comparison with 2.
Ans: The tax cut shifts IS curve to the right, economy under inflationary pressure, the reduction in energy price shift PC curve to the right (cost reduced, AS increase, PC shift to the right wrt to output). Change in inflation is zero. Y ↑, r same, C ↑, I and S uncertain. See drawing below.
and 
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