Chapter 14
Equilibrium

We summarize all the assumptions and conclude the model using the money market equilibrium, i.e. the supply of money Ms corresponds to the demand for money Md. The idea behind this last assumption is that in the event of a temporary imbalance, e.g. due to a monetary policy measure, the economic parameters are adjusted so that the economy moves back towards equilibrium.

Ms = Md Ms = kPy Ms = kSPy S = Ms kPy (14.1)

The exchange rate is thus determined by the domestic money supply, the domestic GDP, the cash coefficient, and the foreign price level. If one of these variables changes, the equilibrium adjusts accordingly.

  1. An increase in domestic money supply by x% causes the currency to depreciate by x% .
  2. An increase in domestic real GDP by x% causes the currency to appreciate by x% .
  3. An increase in the foreign price level by x% causes the currency to appreciate by x% .

The identical rates of change measured in percent are a consequence of the multiplicative structure of equation 14.1.An increase of x% means a multiplication of the corresponding value by 1 + x 100. So if c.p. the money supply increases by x% (MsMs 1 + x 100), then on the left side S must also be multiplied by the factor 1 + x 100, i.e. it also increases by x%. If, on the other hand, there is economic growth of x%, then the factor 1 + x 100appears in the denominator and the left side must be multiplied by 1 1+ x 100. Because 1 1+ x 100 1 x 100, this corresponds to a decrease of S by x%, i.e. an appreciation.

This can also be illustrated by a logarithmic approximation. Here ϕxdenotes the growth rate of variable x in %.

log S = log Ms kPy = log Ms log k log P log y log S 1 + ϕS 100 = log Ms 1 + ϕMS 100 log k 1 + ϕk 100 log P1 + ϕP 100 log y 1 + ϕy 100 log S + log 1 + ϕS 100 = log Ms + log 1 + ϕMS 100 log k + log 1 + ϕk 100 log P + log 1 + ϕP 100 log y + log 1 + ϕy 100 = log Ms log k log P log y log S + log 1 + ϕMS 100 log 1 + ϕk 100 log 1 + ϕP 100 log 1 + ϕy 100 log 1 + ϕS 100 = log 1 + ϕMS 100 log 1 + ϕk 100 log 1 + ϕP 100 log 1 + ϕy 100

Because log 1 + x 100 x 100, this simplifies to

ϕS = ϕMS ϕk ϕP ϕy.

Thus, the devaluation rate of the exchange rate ϕS corresponds exactly to the money growth rate minus the rate of change of the cash coefficient (changes in the monetary process), the foreign inflation rate and economic growth.


(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de