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Inflation and the Exchange Rate: The Role of Aggregate Demand Elasticity

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Abstract

This paper examines the effect of aggregate demand elasticity on the exchange rate when inflation occurs. We discover that both the source of the inflation, whether demand-pull or cost-push, and the elasticity of aggregate demand with respect to the price level, are of consequence for the exchange rate. We obtain two primary conclusions. First, the effect on the exchange rate of cost push inflation is ambiguous and is partially determined by the price level elasticity of aggregate demand. In particular, and assuming that the two examined countries have equivalent aggregate supply elasticities, we conclude that the nation with the less elastic aggregate demand function will see its currency appreciate relative to the other. Second, demand-pull inflation results in an unambiguous increase in the exchange rate but the size of that increase is partially a function of aggregate demand elasticity. Assuming again that two countries have equivalent aggregate supply elasticities, that country with the more elastic aggregate demand will experience currency appreciation.

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Notes

  1. 1.

    The analysis which follows is in the spirit of other “Monetary Approach …” models, including Frenkel (1976) and Bilson (1978), along with those discussed in Boughton (1988).

  2. 2.

    The classic references on the role of price expectations for the behavior of aggregate supply are Friedman (1968) and Lucas (1972). A recent approach to modelling aggregate supply focuses on potential output and the output gap and augments a standard production function with an inflation equation which relates inflation in the current period partially to long-run inflation expectations. For more detail on the “unobserved components model” of the economy’s supply side see Reifschneider, Wascher, and Wilcox (2015), Fleischman and Roberts (2011) and Kuttner (1994).

  3. 3.

    This conclusion also holds in the long-run when b 1 = e 1 = 0. When these parameters approach infinity, however, relative inflation and the equilibrium exchange rate are constant.

  4. 4.

    This conclusion also holds in the long-run when b 1 = e 1 = 0. When these parameters approach infinity, however, the equilibrium exchange rate is constant.

  5. 5.

    In the long run, when b 1 = e 1 = 0, equal growth rates of the nominal money supplies in the two countries will result in equal changes of the price levels and inflation rates and therefore no change in the equilibrium exchange rate. In the extreme Keynesian case, when b 1 = e 1→∞, monetary growth would cause no change in the price level of either country and therefore no change in the equilibrium exchange rate.

References

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Author information

Correspondence to Ben L. Kyer.

Appendix

Appendix

Now, set the respective exogenous price expectations and supply shock variables dαe, dγ, and dγf equal to zero and assume that the countries’ nominal money growth rates are positive and equal to an arbitrary constant, dM = dM f = dM  > 0. These obtain:

$$ d\pi = \left[\frac{\delta {\displaystyle {P}_f}}{\delta {\displaystyle {M}_f}} - \frac{\delta P}{\delta M}\right]d\overline{M} $$
(1A)

Substituting for δPf/δMf and δP/δM with derivatives obtained from Eqs. (7f) and (7) and rearranging terms results in the following solution for dπ/dM:

$$ \frac{d\pi }{d\overline{M}} = \frac{{\displaystyle {a}_1}}{{\displaystyle {a}_2}-{\displaystyle {b}_1}} - \frac{{\displaystyle {c}_1}}{{\displaystyle {c}_2}-{\displaystyle {e}_1}}\kern0.5em \frac{>}{<}\kern0.5em 0 $$
(2A)

Equation (2A) reveals that the change in the exchange rate which results from equal nominal money supply increases in the two countries depends upon the price level elasticities of both aggregate demand and aggregate supply in the nations as well as the respective income velocities of money. For convenience, and to isolate the impact of aggregate demand elasticity on the exchange rate, let the income velocity of money equal one for both countries, i.e., a 1 = c 1 = 1, and assume that the price level elasticities of aggregate supply in the two nations are also equal, b 1 = e 1 > 0. These assumptions imputed to Eq. (2A) produce:

$$ \begin{array}{c}\frac{d\pi }{d\overline{M}} = \frac{1}{{\displaystyle {a}_2}-{\displaystyle {b}_1}} - \frac{1}{{\displaystyle {c}_2}-{\displaystyle {e}_1}}\ \frac{>}{<}\ 0,\kern0.75em if\ {\displaystyle {c}_2}-{\displaystyle {e}_1}\ \frac{>}{<}{\displaystyle {\ a}_2}-{\displaystyle {b}_1}\\ {}\kern8em ,\left|{\displaystyle {a}_2}\right|\ \frac{>}{<}\ \left|{\displaystyle {c}_2}\right|\end{array} $$
(3A)

The interpretation of Eq. (12) is straightforward: for two economies with identical and unchanging short-run aggregate supply conditions and equal growth rates of their respective nominal money supplies, that nation with the more elastic aggregate demand function with respect to the price level will experience both a lower rate of inflation and a corresponding appreciation of its currency. In other words, the exchange rate would fall (rise) under the stated environment. From Eq. (3A) it follows that Cassel’s posited relationship between relative rates of money growth and relative rates of inflation is valid only if the two nations have equal aggregate demand elasticities.Footnote 5

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Kyer, B.L., Maggs, G.E. Inflation and the Exchange Rate: The Role of Aggregate Demand Elasticity. Int Adv Econ Res 22, 1–9 (2016). https://doi.org/10.1007/s11294-015-9544-x

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Keywords

  • Inflation
  • Exchange rate
  • Aggregate demand
  • Elasticity

JEL Categories

  • E00
  • F30