Mundell–Fleming model

The Mundell–Fleming model, also known as the IS-LM-BoP model (or IS-LM-BP model), is an economic model first set forth (independently) by Robert Mundell and Marcus Fleming. The model is an extension of the IS–LM model. Whereas the traditional IS-LM model deals with economy under autarky (or a closed economy), the Mundell–Fleming model describes a small open economy.

The Mundell–Fleming model portrays the short-run relationship between an economy's nominal exchange rate, interest rate, and output (in contrast to the closed-economy IS-LM model, which focuses only on the relationship between the interest rate and output). The Mundell–Fleming model has been used to argue that an economy cannot simultaneously maintain a fixed exchange rate, free capital movement, and an independent monetary policy. An economy can only maintain two of the three at the same time. This principle is frequently called the "impossible trinity", "unholy trinity", "irreconcilable trinity", "inconsistent trinity", "policy trilemma", or the "Mundell–Fleming trilemma".

Basic set-up

Assumptions

Basic assumptions of the model are as follows: Given the approximate formula:

:<math> i = i^\star + \frac{ e' }{e} - 1 </math>

and if the elasticity of expectations <math>\sigma</math>, is less than unity, then we have

:<math> \frac{di}{de} = \sigma - 1 < 0 \quad . </math>

Since domestic output is <math>y = E (i, y) + T(e, y) </math>, the differentiation of income with regard to the exchange rate becomes

:<math> \frac{d y}{d e} = \frac{\partial E}{\partial i} \frac{di}{de} + \frac{\partial E}{\partial y} \frac{dy}{de} + \frac{\partial T}{\partial e} + \frac{\partial T}{\partial y} \frac{dy}{de} </math>

:<math> \frac{dy}{de} = \frac{1}{ 1 - E_{y} - T_{y} } \left( E_{i} \frac{di}{de} + T_{e} \right) \; . </math>

The standard IS-LM theory gives us the following basic relations:

:<math> E_{i} < 0 \; , \quad E_{y} = 1-s > 0 </math>

:<math> T_{e} > 0 \; , \quad T_{y} = - m < 0 \; . </math>

Investment and consumption increase as the interest rates decrease, and currency depreciation improves the trade balance.

:<math> \frac{dy}{de} = \frac{1}{s+m} \left( E_{i} \frac{di}{de} + T_{e} \right) </math>

:<math> \frac{dy}{de} = \frac{1}{s+m} \left( E_{i} ( \sigma - 1 ) + T_{e} \right) \; . </math>

Then the total differentiations of trade balance and the demand for money are derived.

:<math> dT = \frac{\partial T}{\partial e} de + \frac{\partial T}{\partial y} dy = T_{e} de + T_{y} dy </math>

:<math> dL = \frac{\partial L}{\partial i} di + \frac{\partial L}{\partial y} dy = L_{i} di + L_{y} dy </math>

:<math> L_{i} < 0 \; , \quad L_{y} > 0 </math>

and then, it turns out that

:<math> \frac{dT}{dL} = \frac{ T_{e} (s+m) + T_{y} ( E_{i} (\sigma -1) + T_{e} ) }{ L_{i} (\sigma - 1) (s+m) + L_{y} ( E_{i} (\sigma - 1) + T_{e} ) } </math>

:<math> \frac{dT}{dL} = \frac{ T_{e} s + T_{y} E_{i} (\sigma -1) }{ L_{i} (\sigma - 1) (s+m) + L_{y} ( E_{i} (\sigma - 1) + T_{e} ) } \; . </math>

The denominator is positive, and the numerator is positive or negative. Thus, a monetary expansion, in the short run, does not necessarily improve the trade balance. This result is not compatible with what the Mundell–Fleming predicts.

Mundell–Fleming model

Basic set-up

Assumptions

See also

References

Further reading