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)