Macroeconomics

Question 1

PS Curve

Answer 1

dP/P = dW/W
P = (1+u)(W/MPL)
W/P = MPL/(1+u)
rearranges to
W/P = (1-u)MPL

Question 2

WS Curve

Answer 2

W = Pe * B(Zw,N)
dW/W = dPe/pe + alpha(yt-ye)
dW/W = PI t-1 + alpha(yt-ye)

Question 3

PC Curve

Answer 3

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

Question 4

IS Closed Economy

Answer 4

y = A-ar_t-1
y= 1/(1-C1(1-t)) *(C0+a0+G-a1r)

Question 5

Supply shocks that lead to inflation

Answer 5

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.

Question 6

Deflationary supply shocks

Answer 6

Fall in technology or productivity, Less competition. Shifts PS down.
Raising unemployment benefits, strengthened unions, worse working conditions. Shift WS to the left.

Question 7

MR

Answer 7

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

Question 8

Solow Production Function

Answer 8

Y = AK^(α)*N^(1-α)
y=Ak^(α)

Question 9

Break even investment

Answer 9

δk
(δ+n)k
(δ+n+x)k(hat)

Question 10

fundamental Solow equation of growth

Answer 10

k(dot) = s(k)^α - (n+x+δ)k

Question 11

consumption solow

Answer 11

c= (1-s)y

Question 12

Golden Rule

Answer 12

Maximising C
f(K) - (n+δ+x)k
f’(k) - n + δ + x = 0
MPK = n+δ+x

Question 13

Costs of changing s

Answer 13

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.

Question 14

finding capital per effective worker at SS

Answer 14

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)

Question 15

output per effective worker at SS

Answer 15

y= k^α
y(hatdot) = k(hatdot)^α =(s/(δ+n+x)^(α/(1-α))

Question 16

Consumption per effective worker

Answer 16

c(hatdot) = (1-s)y(hatdot)
c(hatdot) =(1-s)(s/(δ+n+x)^(α/(1-α))

Question 17

Capital per effective worker symbol and growth rate at SS with technology

Answer 17

k(hat) = K/AN at the ss growth = 0

Question 18

Output per effective worker symbol and growth rate at SS with technology

Answer 18

y(hat) = Y/AN at the ss growth = 0

Question 19

Output per worker symbol and growth rate at SS with technology

Answer 19

k = K/N at the ss growth = x

Question 20

Total output symbol and growth rate at SS with technology

Answer 20

Y = y(hat) * N * A at the ss growth = n + x

Question 21

An increase in the multiplier

Answer 21

makes the Keynesian cross y curve steeper and the IS curve flatter.

Question 22

Types of expectations

Answer 22

adaptive Expectations = π(expected) = π t-1
Rational expectations = π(expected) = πt on average.
PC becomes, πt = π(expected) + α(yt-ye) + error

Question 23

Credibility modelling

Answer 23

χπ(target) + (1-χ)πt-1 +α(yt-ye)

Question 24

If the CB sets MR above target

Answer 24

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)

Question 25

Exchange rates

Answer 25

nominal exchange rate: e
Real exchange rate: Q = (eP)/P, P = price of foreign goods, P = price of domestic goods.

Question 26

appreciation/Depreciation

Answer 26

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.

Question 27

Open economy IS

Answer 27

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

Question 28

Simplified IS Open Economy

Answer 28

y = A - art-1 + bqt-1

importers and investors face a 1 year lag

Shift factors, q, A, b

Question 29

Inflation in the Open Economy

Answer 29

CB and wage setters consider domestic inflation only.

Question 30

Open Economy Assumptions

Answer 30

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.

Question 31

UIP condition

Answer 31

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

Question 32

ERU

Answer 32

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.

Question 33

AD

Answer 33

y= A - ARt-1 + bq,
drawn in the y,q space.
Shift factors, A and r, a

Question 34

Real UIP condition

Answer 34

ri - r* = q(expected) - qt

Question 35

Supply shock in the open economy

Answer 35

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.

Question 36

RX curve

Answer 36

The set of optimising interest rate, y combinations for all IS curves.

Question 37

At MRE

Answer 37

The Domestic interest rate = world interest rate
domestic exchange rate = expected exchange rate
y=ye
inflation=target
AD=ERU

Question 38

Convergence

Answer 38

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.