IS LM models Flashcards
we had assumed up until now that investment was exogenous, but what is it dependent on ?
income and interest rates
I = I ( Y , i )
( + , - ) relationships
how does the Z equation look when we include this I into it ?
Z = Y = C ( Y - T ) + I ( Y , i ) + G THIS IS THE IS RELATION
= C0 - C1.T + B0 + G - B2 .I + B1.Y + C1.Y
Abar = C0 - C1.T + B0 + G
Z = Abar - B2 .I + B1.Y + C1.Y
y intercept + ( B1 + C1 ) .Y
what is the equation for investment ?
I = b0 + b1.Y - b2.i
b0 - autonomous investment
b1 - relationship between income and investment
b2 - relationship between i and I sensitivity parameter
what is income equilibrium in this market ?
Y = Abar - B2 .I + (B1 + C1 ) . Y
Y - (B1 + C1 ) . Y = Abar - B2 .I
Y ( 1 - (B1 + C1 ) ) = Abar - B2 .I
Y* = 1 / ( 1 - (B1 + C1 ) . ( Abar - B2 . I )
which part of the income equilibrium equation is the multiplier ?
1 / ( 1 - (B1 + C1 )
when there is a change in A bar ( at the given level of i ) how do you calculate the change in Y* ?
changeY* = multiplier . change ( Abar - b2 . i )
how do you derive the IS curve ?
when you lower i AD shifts upwards and there is a new, equilibrium in the goods market, for a bigger Y .
the IS curve shows the convex curve and negative relationship between i and Y
at every point in the IS curve , the goods market is in equilibrium.
what shifts the IS curve ?
changes in fiscal policy
- taxes increase , IS curve shifts inwards
- gov spending or transfer payments increase , IS curve shifts outwards
because at every existing i , income has changed - this leads to bigger economical changes
what is the LM relation ?
it is where the money market is in equilibrium.
equilibrium in M = £Y.L(i)
but to reflect real money it must be divided by the price level.
M/P = Y.L(i)
how do you construct the LM curve ?
traditionaly there is a complex curve but it reflects the wrong relationship in reality. where Md changes so i does.
in reality i is set by the government and the CB adjust supply of money to account for the changes in demand.
the actual LM curve is on an axis with Y on the bottom and IR on the vertical axis
the LM curve is a horizontal line set exactly where the policy rate i
i = i bar
what does the point in the IS,LM model where the two curves cross mean ?
it is the point at which both the money and goods markets are in equilibrium.
the model shows what happens to i or Y when the markets move away from equilibrium.
how does ……… policy effect the is lm model ?
a. fiscal
b. monetary
a.
contractionary - IS shifts inwards - income falls - i bar stays constant
expansionary - IS shifts outwards - income rises - i bar stays constant
b.
contractionary - LM shifts down - income falls - i bar shifts down
expansionary - LM shifts upwards - income rises - i bar shifts up
what are some advantages to policy mixing when needing to effect the islm model ?
- could prevent falls in income
- using too many exp. fiscal policy, there will be a fall in gov. revenue. and a rise in the budget deficit which could lead to large amounts of debt
- when i bar is low enough it becomes ineffective to use monetary policy and therefore we must overuse it or we will lose that monetary tool.
- must analyse what you want to do to the composition of GDP and apply the policy mix needed.
up until now we have assumed that there was only one IR - determined by monetary policy.
but in reality there are many set up by different people. give some examples ?
commercial to commercial bank rate - prime lending rate (public)
central bank to commercial base rate - GBP LIBOR RATE
what are the nominal and real IRs and how do you adjust from nominal to real ?
nominal IR - in terms of currency
real IR - in terms of baskets of goods
you must adjust to take into account expected inflation
nominal / price level = real
what is the formula for nominal IR ( i.e. what do you pay back when you borrow £ ) ?
borrow £
pay back £(1 + it) at the end
say the price of some good now is Pt and expected price in a year is Pet+1. and we borrow this exact amount to buy the good, how much do we re pay in one year ?
(1 + rIRt) = (1 + it) Pt / Pet+1
if inflation is to be expected
pieet+1 = Pet+1 - Pt / Pt
how do we adjust the expected price level in the equation for repaying in one year ?
(pieet+1)+1 =(Pet+1 - Pt / Pt)+1
(pieet+1)+1 =(Pet+1 / Pt) + 1 - 1
(pieet+1)+1 =(Pet+1 / Pt)
invert:
1 / (pieet+1)+1 = (Pt / Pet+1)
then we can substitute this into the equation
1 + rt = (1 + rIRt) = (1 + it) . 1 / (pieet+1)+1
we don’t actually use this approximation unless inflation is bigger than 20%. we use an approximation. what is it ?
rt = it - pieet+1
what are the implications of this, ?
- when pieet+1 = 0 the nominal and real rate are equal
- because expected inflation is normally positive, real IR is normally lower than nominal IR
- for a given nominal IR, the higher the expected inflation the lower the real rate will be
- nominal IR can’t be lower than 0 but real can
while the CB determines the nominal IR it also takes real into account because it affects spending. the CB set nominal based on what they want real to be. if the CB wants rate R real what do they set i to ?
nominal IR = R + expected inflation
some bonds are risky so holders require a risk premium. what is the equation to get the same expected return on a risky and riskless ?
1 + i = (1-P)(1+i+x) + P(0)
X = (1+i)P / 1-P
P higher - X higher
1 + i - nominal IR
X - risk premium
P - probability of defaulting
what is direct finance ?
borrowing directly between the ultimate lenders and borrowers.
until now we have discussed direct finance when in reality there are financial intermediaries or institutions such as banks, hedge funds, money market funds or mortgage companies.
what is leverage ?
financial intermediaries borrow at low rates and lend at higher rates to make a profit
what is the equation for capital ?
capital = assets - liabilities
what is the capital ratio ?
capital : assets
what is the leverage ratio ?
assets : capital this is highly interchangeable but more used
the higher the leverage ratio
a. how is the expected profits effected ?
b. how is risk effected ?
a. the higher the expected profits because you get more assets for your liabilities / capital
b. higher risk as if the assets default, you owe more money
what is insolvency ?
assets < liabilities - causes bankruptcy
banks must ensure they have enough capital and capital ratio to prevent damage from falls in asset value.
what is liquidity ?
availability of liquid ( easily cashed out ) assets.
the lower the liquidity of assets the higher the risk of insolvency and bankruptcy (also risk of fire sales). why ?
if investors doubt asset value - loans get called back from banks - borrowers normally don’t have the cash to pay straight away - must sell but this is tricky as the information may not be clear - end up at the fire sale / not sold at all - insolvency and bankruptcy
the lower the liquidity , how does this effect the level of risk and why ?
the higher the risk as the investor can withdraw whenever they want ( e.g. liquid checking deposit account )
what are some major economic consequences of bankruptcy ?
- falls in confidence ( bank runs )
- falls in spending
- falls in AD / GDP
- worsen originally bad climate
now that we have clear distinctions between nominal vs real IR and policy rate vs public IR. what are the IS and LM relations now ?
IS = Y = C(Y-T)+I(Y,i-piee+x) + G
LM = i = i bar
the LM equation uses policy rate (nominal) by CB
the IS equation - uses borrowing rate (real)
what is the lowest that i bar can be ?
negative of inflation ( - piee)
if we assume that because the CB chose a certain i to achieve a certain R, that the just chose R straight away. how does this effect the is and lm relations ?
IS = Y = C(Y-T)+I(Y, r +x) + G
LM = r = r bar
suppose the risk on an investment increases because of bankruptcy or investors just become more risk averse. this causes the IS to fall and how should the government deal with the fall in income ?
we could use fiscal policy to shift is back to original and increase income.
we could use monetary policy to reduce r bar and raise income but in some cases the r bar would need to be - in order to achieve a certain ( or original ) level of income and the nominal ir has a zero lower bound and becomes less effective the lower it is.
