#### 21.1.1 The Mundell-Fleming model

The Mundell-Fleming model is suitable for short- and medium-term predictions. This can be deduced from the assumptions it is based on.

1. Horizontal goods supply curve
• Prices and wages are constant
• cf. Keynes paradigm
• Simplification: ${P}^{\ast }=P=1$ so that $Q=\frac{S{P}^{\ast }}{P}=S$
2. Short-term analysis: current account
• Current account surplus $B=B\left(y,Q\right)=B\left(y,S\right)$
• $\frac{\mathit{dB}}{\mathit{dS}}={B}_{s}>0$ : Current account surplus B reacts positively to the real exchange rate (competitiveness)
• $\frac{\mathit{dB}}{\mathit{dy}}={B}_{y}<0$ : and negatively to the real GDP (consumption effect)
3. Finite capital flows
• Finite interest rate elasticity of international capital flow
• A change in the interest rate differential leads to finite capital inflows and outflows $K$
• E.g. risk-averse capital market stakeholders
• $r\ast$ is exogenous
4. Static exchange rate expectations
5. Entirely flexible exchange rates: constant equilibrium of balance of payments (BoP)
 $\underset{F\left(y,S,r\right)}{\underbrace{B\left(y,S\right)+K\left(r\right)}}=0$

with ${F}_{y}<0,{F}_{s}>0,{F}_{r}>0$

ad 1) The assumption of a horizontal supply curve implies that the model economy is in a situation of underutilization, as was the case in Keynes’ famous analysis for the time of the Great Depression. Another reason could be that such a short time horizon (up to one year) is considered, that general prices cannot adjust due to their inertness. To simplify matters, we normalize the prices to 1 so they drop out of the formulas and the real and nominal exchange rates coincide.

ad 2) The central analytical instrument in the Mudell-Fleming model is the current account $B$. This does not have to be in equilibrium, but it shows the state of the economy and thus determines the net capital flows. (see (5)). The current account is influenced by two key variables: the national income and the exchange rate. If the real exchange rate increases (depreciation), then domestic goods abroad become cheaper. Therefore, the competitiveness of the domestic industry increases and net exports increase ($\frac{\mathit{dB}}{\mathit{dS}}={B}_{s}>0$). If domestic wealth (GDP) increases, people buy a disproportionately large amount of foreign goods5 ($\frac{\mathit{dB}}{\mathit{dy}}={B}_{y}<0$).

ad 3) The capital account $K\left(r\right)$ reacts to the difference in interest rates at home ($r$) and abroad (${r}^{\ast }$). Since we assume the foreign interest rate to be exogenous, the domestic interest rate $r$ remains as a variable. If interest rates rise, investment in the home country becomes more attractive and capital flows in. The capital account increases ($\frac{\mathit{dK}}{\mathit{dr}}={K}_{r}>0$). The interest rate elasticity of the international capital flow $\frac{\mathit{dK}}{\mathit{dr}}\frac{r}{K}$ is finite. That means, a change in the interest rate differential leads to finite capital inflows or outflows $K$ Therefore, interest rate differences can remain.6 The reasons for the finiteness of the interest rate elasticity can be transaction- and information- costs, time, regulatory measures (e.g. different chargeability in risk classes) and, above all, risk aversion (at least there is the exchange rate risk) for international capital investors.

ad 4) One of the assumptions is the static, i.e. fixed, exchange rate expectation. Similar as for the interest rate parity theory, it can be criticized that shocks can change the long-term equilibrium (at least for nominal sizes) and thus have an impact on the long-term exchange rate as well as on its expectations. Even if the Mundell-Fleming model is only used for short-term analysis, the impact of the examined shocks on the long-term equilibrium parameters, which are considered to be exogenous, can, of course, distort the result. Thus, the potential impact on the long term must be examined with each analysis.

ad 5) In the standard model, we assume a free capital and foreign exchange market without interventions, i.e. the exchange rates adapt very quickly to market developments. Under these conditions, the equilibrium of the balance of payments persists. The balance of payments $F$ is the sum of the current account $B$ and the capital account $K$, and thus depends on the three variables income $y$, exchange rate $S$ and interest rate $r$ . $F\left(y,S,r\right)=B\left(y,S\right)+K\left(r\right)=0$ Within the Mundell-Fleming model - as usual in these models - the exchange rate is quoted in price, i.e. $S$ is the price of one unit of foreign currency measured in domestic currency. For example, the exchange rate $S=0,8\frac{e}{}$ means for an European that the price for one US dollar is 0.8. Therefore, in price quotation, an increase of $S$ means depreciation of the domestic currency.

ATTENTION: Usually the stock exchange uses the quantity quotation, i.e. exactly the reciprocal value.

5Possible reasons are that the propensity to work decreases with increasing income, or that foreign goods are considered to be more luxurious and therefore more appropriate to higher levels of prosperity.

6In the case of infinite interest rate elasticity, any difference in the interest rate would be instantly compensated, since a country with higher interest rates would immediately have capital inflows (in infinite amounts), so that the increased capital supply would make interest rates decrease and in the country with the reduced capital supply, interest rates would rise to the same level.

(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