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If an economy grows, due to a tax reduction for example, how does that affect the exchange rate?

My logic would be that reduced taxes put more money into people's pockets, which they then use to buy more stuff. If all of that stuff were produced domestically, nothing were to happen to the exchange rate. If some of that stuff were to be produced in other countries and imported, those importing the goods will want to exchange the domestic currency for their foreign currency. That would increase demand for foreign currency relative to domestic currency and thereby decrease the value of the domestic currency.

However, as the economy grows other country's producers will want to buy into the economy's market, for which they will need that country's currency and increase demand for it. That will drive the currency up.

Therefore: What effect is stronger in response to domestically motivated economic growth? Is it the depreciating effect of imports or the appreciating effect of new entrants or am I missing something entirely?

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What effect is stronger in response to domestically motivated economic growth? Is it the depreciating effect of imports or the appreciating effect of new entrants or am I missing something entirely?

There's no general answer to that. It depends on the particulars of each economy. Some factors are:

  • Whether imports outweigh exports or viceversa;
  • Whether the tax reduction is coupled with spending cuts, tariffs, foreign debt, etc.;
  • Taxpayers' general propensity to save the additional "disposable" income could influence the exchange rate in either direction, depending on where they deposit their savings.
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There is a small catch in your explanation. If the domestic demand increases relative to foreign demand, hence domestic price level will also increase. It will have following effects:

1) Since, inflation differential is a major determinant of the exchange rate, hence due to higher inflation the domestic currency will depreciate.

2) Exporters have an incentive to reduce Exports because domestic price level and demand is higher and so is the revenue. The goods which were previously exported now will be sold in the domestic market.

Either way the currency will depreciate.

Now the question depends upon the new entrants.

I think it is better to do a micro-economic analysis here.

  • If the market is competitive then surely the new entrants do not face any barriers to entry.
  • If the market is oligopolistic or government follows protectionist policy for its domestic industries then surely there is no way for the new entrants to make their way in.

In my opinion, there are even more factors which you're missing:

  • Depreciation on appreciation is a short run and medium run phenomenon. The timing involved for the exporters and importers to adjust according to fluctuations in domestic demand is far less than that required for new entrants to establish their production in the country.
  • Plus there is one more dynamic involved here. You are completely ignoring the role of expectations. Investment does not depend on current prices(demand) but on the expectations regarding future prices(demand).
  • What if the country is politically unstable or faces a high variability in demand. Thus, it is not a good place for investors. Hence new entrants will never come in.
  • The other part you are missing is, the cost of production involved. What if higher demand comes with higher wage rates (Wage-price spiral). The higher demand does promise a greater revenue but not lower costs and profits are the function of both revenue and costs.
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