W2P5 - Overshooting model

Question 1

A small open economy with perfect capital mobility is characterised by the following equation:
Mt/Pt = 2Y¯ - 1000i(t)

Explain the intuition behind it.

Answer 1

This equation is the money market equation that links real money supply with real money demand. In this case we assume that real money
demand only depends positively on income Y¯ which we assume to be exogenous and negatively on nominal interest rates i(t). The money market equation is assumed to be a short-run relationship as financial
markets are quickly adjusting.

Question 2

A small open economy with perfect capital mobility is characterised by the following equation:
i(t) = i* - (S(t+1) - S(t)) / S(t))

Explain the intuition behind it.

Answer 2

The equation is the uncovered interest parity condition that links nominal exchange rates with nominal domestic and foreign interest rates. The UIP condition is a short-run relationship as financial markets are
quick to adjust.

Question 3

A small open economy with perfect capital mobility is characterised by the following equation:
σ = SP/P*

Explain the intuition behind it.

Answer 3

The equation is the purchasing power parity condition. PPP only
holds in the long-run as prices are sticky i.e. slow to adjust.

Question 4

Describe the PPP and MM schedule in the overshooting model

Answer 4

S is on the vertical axis
P is on the horizontal axis
PPP is a downward sloping curve
MM is an upward sloping line
Where PPP and MM intersect at point A (coordinates are (P(0), S(0)), there is a vertical line going through the intersect called P(LR)

Question 5

What is useful to know about interest rates and foreign interest rates in the long-run?

Answer 5

in the long-run domestic interest rates equal foreign interest rates:
i = i*

Question 6

What are the steps of working out the long-run equilibrium if you know the following:
Mt/Pt = 2Y¯ - 1000i(t) ( AKA money market equation)
i(t) = i* - (S(t+1) - S(t)) / S(t)) (AKA UIP condition)
In the long-run, purchasing power parity
holds so that
σ = SP/P* (aka PPP condition)

Exogenous variables:
M(t) = 400
Y¯ = 120
i*=0.04

Answer 6

step 1 = use the money market condition and recall that in the long-run domestic interest rates equal foreign interest rates (i=i*)
step 2 = sub all known vals into the money market equation
step 3 = make Pt the subject
step 4 = recall that in the long run PPP needs to hold and work out the PPP condition
step 5 = make S the subject
Step 6 = you should have the long-run equilibrium for the endogenous variables as P = 2,
S = 2.4, and i = 0.04