Macroeconomics Flashcards
PS Curve
dP/P = dW/W
P = (1+u)(W/MPL)
W/P = MPL/(1+u)
rearranges to
W/P = (1-u)MPL
WS Curve
W = Pe * B(Zw,N)
dW/W = dPe/pe + alpha(yt-ye)
dW/W = PI t-1 + alpha(yt-ye)
PC Curve
setting equality between WS and PS.
dP/P = dP/P(expected) + alpha(Yt-Ye)
πt = πEt + α(yt-ye)
Shows the feasible set of inflation and output pairs for a given lagged inflation rate. Need to be drawn through the equil y and last period’s inflation
IS Closed Economy
y = A-ar_t-1
y= 1/(1-C1(1-t)) *(C0+a0+G-a1r)
Supply shocks that lead to inflation
Improvement of technology and productivity, Shifts PS upwards. More competition, shifts the PS unwards as PS approaches MPL as u falls.
Lower unemployment benefits, shiffts WS to the right. An improvement in working conditions, a reduction in union power.
Deflationary supply shocks
Fall in technology or productivity, Less competition. Shifts PS down.
Raising unemployment benefits, strengthened unions, worse working conditions. Shift WS to the left.
MR
derived from CB loss function
L = (yt-ye)^2+β(πt-πtarget)^2
(yt-ye) = -αβ(πt-πtarget)
(πt-πtarget) = (1/-αβ)*(yt-ye)
β=1 balanced
β>1 inflation adverse
β<1 unemployment adverse.
α labour sensitivity to unemployment.
slope = -1/αβ
Solow Production Function
Y = AK^(α)*N^(1-α)
y=Ak^(α)
Break even investment
δk
(δ+n)k
(δ+n+x)k(hat)
fundamental Solow equation of growth
k(dot) = s(k)^α - (n+x+δ)k
consumption solow
c= (1-s)y
Golden Rule
Maximising C
f(K) - (n+δ+x)k
f’(k) - n + δ + x = 0
MPK = n+δ+x
Costs of changing s
political costs of increasing taxes, reducing spending
Short term loss in consumption,
political cost of losing output overall if the current point is too high.
finding capital per effective worker at SS
sf(k(hatdot))-(δ+n+x)k = 0
sk^α = (δ+n+x)k
s = (δ+n+x)k^(1-α)
k = (s/(δ+n+x))*(1/1-α)
output per effective worker at SS
y= k^α
y(hatdot) = k(hatdot)^α =(s/(δ+n+x)^(α/(1-α))
Consumption per effective worker
c(hatdot) = (1-s)y(hatdot)
c(hatdot) =(1-s)(s/(δ+n+x)^(α/(1-α))
Capital per effective worker symbol and growth rate at SS with technology
k(hat) = K/AN at the ss growth = 0
Output per effective worker symbol and growth rate at SS with technology
y(hat) = Y/AN at the ss growth = 0
Output per worker symbol and growth rate at SS with technology
k = K/N at the ss growth = x
Total output symbol and growth rate at SS with technology
Y = y(hat) * N * A at the ss growth = n + x
An increase in the multiplier
makes the Keynesian cross y curve steeper and the IS curve flatter.
Types of expectations
adaptive Expectations = π(expected) = π t-1
Rational expectations = π(expected) = πt on average.
PC becomes, πt = π(expected) + α(yt-ye) + error
Credibility modelling
χπ(target) + (1-χ)πt-1 +α(yt-ye)
If the CB sets MR above target
Loss function changes
L = (yt-yH)^2 + β(πt-πtarget)^2
so MR changes from
(yt-ye) = -αβ(πt-πtarget)
to
(yt-yH) = -αβ(πt-πtarget)
at MRE, yt=ye, so
(ye-yH) = -αβ(πt-πtarget) (both positive)
πt = πtarget + (1/-αβ) *(ye-yH) ( rearranged)
Exchange rates
nominal exchange rate: e
Real exchange rate: Q = (eP)/P, P = price of foreign goods, P = price of domestic goods.
appreciation/Depreciation
if e goes up thats a deprecaition, if e goes down thats an apprecaiiton.
If Q goes up thats deprecaition as foreign goods have become more expensive relative to domestic goods. Q is a measure of price competitiveness.
Open economy IS
y = C + I + G + NX, Where NX = exports - imports,
NX = b0 - b1y + b2q
where q = log(Q)
b0: exogenous determinants of imports, tastes trade barriers etc
b1: marginal propensity to import
b2: Sensitivity of NX with respect to changes in q
y= 1/(1-C1(1-t)+b1) *(C0+a0+G+b0-a1r+b2q)
in the open economy a change in q can shift the IS. A depreciaiton will make home goods relatively cheaper, stimulating exports.
Spending multiplier is smaller as imports are an additonal leakage. Slope of the IS is also steeper
Simplified IS Open Economy
y = A - art-1 + bqt-1
importers and investors face a 1 year lag
Shift factors, q, A, b
Inflation in the Open Economy
CB and wage setters consider domestic inflation only.
Open Economy Assumptions
perfect international capital mobility
home economy is small and so cannot influence world interest rate or foreign prices
only two assets, money and bonds.
Foriegn and domestic bonds are perfect substitutes, ie, no difference in risk etc.
UIP condition
The gain in interest from holding home currency instead of foreign bonds = the loss from expected depreciation of home currency against the US dollar.
It = i* + (e(expected)-et)/et
et is endogenous, i* = Foreign nominal interest rate, I= domestic interest rate
it - i * = (e(expected)-et)/et, if either side is positive then a depreciation is expected, if either side in negative then an appreciation is expected. after all trading has ceased.
it-i* = loge(expected)-loget.
real terms:
rt-r* = qE - qt
ERU
Equilibiurm rate of unemployment. Determined by the intersection of WS and PS curves. To the right of ERU, upwards pressure on inflation. To the left, downwards pressure on inflation. On the ERU inflation is constant.
it is drawn on the q, y space, it represents the locus of points where there is supply-side equilibrium.
AD
y= A - ARt-1 + bq,
drawn in the y,q space.
Shift factors, A and r, a
Real UIP condition
ri - r* = q(expected) - qt
Supply shock in the open economy
when the markets are in MRE. The new equilibrium in the labour market results in a new ERU. Depending on the type of supply side shock, real wages will either rise fall or stay the same. If the ERU shifts to the right, since the AD is upwards sloping there will be an increase in q, aka a depreciation. If the ERU shifts to the left there will be a fall in q a.ka a depreciation.
RX curve
The set of optimising interest rate, y combinations for all IS curves.
At MRE
The Domestic interest rate = world interest rate
domestic exchange rate = expected exchange rate
y=ye
inflation=target
AD=ERU
Convergence
To find evidence of convergence we must find the growth rate of capital per worker
k(dothat) = sf(k(hat)) - (δ+n+x)k(hat)
divide by k(hat)
k(dothat) / k(hat) = sf(k(hat)) / k(hat) - (δ+n+x)k(dot)/ k(hat)
f(k(hat)) / k(hat) = APK
Since APK is larger for lower levels of output, capital per effective worker grows faster at lower levels of k.
