# Why does this example illustrating the effect of growth on exchange rates not work?

I'm looking for a (very) elementary explanation for why economic growth leads to one's currency becoming more valuable. This certainly seems like it should happen (example: "An economy experiencing growth results in a currency appreciating, and the exchange rate adjusts accordingly.")

Suppose I wall off my house, declare independence, and issue my own currency ("spooks"). Because one can't buy anything with spooks, they are literally worthless.

Now suppose I make a burger, which I sell for 1 spook. If the burger is worth 2 USD (i.e. one can buy a very similar burger for 2 in the US), then that fixes an exchange rate 2 USD = 1 spook. I now make ten burgers, therefore growing my economy 10x. But the burgers are still only worth 2 USD each, so the exchange rate is still 2 USD to 1 spook.

Why does economic growth in this example not increase the value of my currency? It seems very probable that the example is oversimplified, in which case I'm looking for a simple example that nonetheless captures how economic growth leads to a currency appreciating.

• The statement "economic growth leads to one's currency becoming more valuable" does not seem to be true in general, and the definition of 'valuable' is a little vague. Please clarify what exactly you mean by 'valuable' (purchasing power or increasing exchange rate w.r.t. another currency? Please don't write both) and support your claim with a reference (it does not have to be an elementary explanation). Until you do this I don't think you can find a good explanation, much less a very elementary one. Nov 9, 2023 at 8:04
• A bit further elucidation on why I think "economic growth leads to one's currency becoming more valuable" is clearly not generally true: there are many years when both the USA's and China's economy grow. But clearly, it is impossible that both the dollar appreciates w.r.t. the renminbi and the renminbi appreciates to the dollar. In this argument I did not even touch on monetary policy. Nov 9, 2023 at 8:06
• @Giskard "valuable" means increasing exchange rate w.r.t another currency, Reference is in the OP. Explanation certainly seems intuitive - if you produce more goods, then other people will need more of your currency to buy those goods, hence the exchange rate goes up. In the US vs. China case, presumably if the Chinese economy grows more than the US economy does, the RMB appreciates vs. the USD. Nov 9, 2023 at 8:25
• "presumably if the Chinese economy grows more than the US economy does, the RMB appreciates vs. the USD" Okay, if I refute your premise by showing you time periods when this is not the case, will you accept the answer? Nov 9, 2023 at 9:27
• @Giskard see the OP, there is a link: investopedia.com/terms/c/currency-appreciation.asp Nov 9, 2023 at 9:42

Why does economic growth in this example not increase the value of my currency? It seems very probable that the example is oversimplified, in which case I'm looking for a simple example that nonetheless captures how economic growth leads to a currency appreciating.

Because you are de facto on fixed exchange rate.

Under flexible exchange rate value of a currency depends on multiple factors. Let just take simplistic monetary model of exchange rate given by:

$$\ln S= \ln(m)- \ln(m_f) -(\ln(y)-\ln(y_f))+\lambda(i-i_f)$$

where $$S$$ is the exchange rate $$m$$ is the money supply, $$y$$ real output, $$i$$ interest rate and $$f$$ denotes foreign country (variables without $$f$$ are home country variables). This is not necessary even the most accurate model since we can add expectations and things like scapegoating in and so on. So in real life flexible exchange rate depends positively on real economic output but also on multitude of factors unrelated factors that can offset the effect of real economic output. This is what the other two answers are talking about.

However, you are de facto on fixed exchange because of your assumptions. Exchange rate can also be expressed under the law of one price as: $$S= P/P_F$$, where $$P$$ is price level. In real life, law of one price can be violated due to transaction costs, transportation costs, tariffs and so on. But in your example you ignore all such things so law of one price applies.

In your example, there is only 1 good so price level is fully determined by that 1 good. Next you decided to arbitrary fix both price in US and in your made up country. Hence you fixed the exchange rate purely by your assumptions.

In real life when country becomes more productive price level adjusts as well. Price level is inversely related to real output, e.g. standard New Keynesain money market equilibrium which determines price level is given by $$P= \frac{M}{L(Y,i)}$$ where $$M$$ is money supply $$L$$ demand for funds/money, $$Y$$ is real output, and $$i$$ nominal interest rate. So as you produce more $$P$$ should decline, and when $$P$$ declines exchange rate appreciates. However, you assumed this adjustment mechanism away in your example, since you just assume the price of the burger is fixed no matter how much you produce which is not necessarily accurate theoretically or even realistically.

Of course, if you just wilfully ignore adjustment mechanisms in other parts of an economy you can get result where nothing happens. This should not puzzle you, in your example output cannot affect exchange rate, because you simply assumed (even if unintentionally) that it can't have any effect on price level.

It has been made clear in the comments that "economic growth leads to one's currency becoming more valuable" this means the exchange rate improves.

While one could argue that ceteris paribus economic growth tends to strengthen an exchange rate, there are many other factors that come into play. Because of this, the claim is too general and not always true. (I am afraid this is frequently the case with Investopedia claims.)

Between 1991 and 2022 there were many years when both the Chinese and the US economy were growing.

Source

Clearly it is not possible that both countries' exchange rate would appreciate with respect to the other, thus Investopedia's claim is false. For the more nuanced claim that relative grow is what determines which way the exchange rate of the currencies go, we again have evidence to the contrary. In the above 1991-2022 period, China always grew at a faster rate then the US, but there were years where its currency appreciated w.r.t. the USD, and years where it depreciated:

Source

As stated earlier, many other factors should be taken into account, such as world events, monetary policy, expectations on future growth, future monetary policy, etc.

• while you are correct in pointing out that exchange rate depends on other factors, the OP example is not related to other factors. Exchange rate is under law of one price given by $S=P/P_f$, in OP made up example he simply fixed both P, and P_f, in OP example there is no friction so law of one price applies and by fixing P and P_f he simply de facto fixed exchange rate. No other factors can even come in play. Even under strict ceteris paribus assumption, the exchange rate won't change in OPs example, since assumptions in OP example make any exchange rate change impossible
– 1muflon1
Nov 9, 2023 at 12:43
• I did not read OP's 'elementary explanation', just their the general claim they were making, which is about the real world, not a model with LoOP. In fact, at the end of their question they specify: "It seems very probable that the example is oversimplified, in which case I'm looking for a simple example that nonetheless captures how economic growth leads to a currency appreciating." Nov 9, 2023 at 14:29

As has been pointed out, economic growth does not make an exchange rate more valuable. Ultimately an exchange rate is just a price, and in economics this is conceptually different from the volume of economic activity, which is a quantity.

If you make 10 burgers, but you sit and eat them by yourself, then at no point has the spook-dollar (SPK/USD) exchange rate come into it.

If you decide to sell (export) those burgers, and you are able to sell all 10 burgers for $2 each, because that's the market price, there are plenty of buyers and sellers in your neighbourhood, and your burgers are no better or worse than any of the other ones, then your sale of 10 burgers is not going to move the SPK/USD exchange rate. If you make your burgers using your grandmother's secret recipe that everyone loves and are willing to pay more than$2 for, than the SPK/USD will appreciate. But that's not because you made more of them, it's because your burgers are so good that you can charge more for them. Conversely, if your burgers are generally quite pathetic and you can only shift them by charging much less for them, than SPK/USD will depreciate.