Determining Equilibrium Exchange Rates

A Simple Model: The Flow Approach

The most intuitive way to think about the foreign exchange (forex) market is as a direct consequence of international trade, which we tracked in the Current Account. This is known as the "traditional flow approach."

• Demand for a currency comes from foreigners who need it to buy the home country's goods and services (exports). If the home currency becomes cheaper (depreciates), its exports become more attractive, so foreigners demand more of its currency. This gives a downward-sloping demand curve.
• Supply of a currency comes from domestic residents who need foreign currency to buy foreign goods and services (imports). They supply their home currency to the forex market to exchange it. If the home currency becomes more expensive (appreciates), foreign goods become cheaper for domestic residents, so they supply more of their currency to buy more imports. This gives an upward-sloping supply curve.

The equilibrium exchange rate is where the quantity demanded equals the quantity supplied.

Because you prefer working with equations, we can model this with simple linear functions. For instance, if the market for US dollars in India has the following demand and supply schedules:

• Quantity Demanded: $Q_d=300-4P$
• Quantity Supplied: $Q_s=-100+6P$

Here, 'P' is the price of a US dollar in Indian Rupees (the exchange rate). We find the equilibrium by setting $Q_d=Q_s$.

This calculation is analogous to the simple price-quantity equilibrium problems we solved in earlier modules.

While this flow model is a useful starting point, it is incomplete. As we saw in the previous lesson, the Financial Account, which tracks asset transactions, involves flows of money that are vastly larger than those from trade. To understand short-run exchange rate movements, we must turn to an asset-based model.

The Asset Market Approach: Exchange Rates as Asset Prices

The modern view treats currencies as financial assets. The decision to hold wealth in dollars, euros, or yen depends on the expected rate of return of assets denominated in those currencies. This is often called the portfolio-balance or asset market approach.

The total return on a foreign asset depends on two things:

1. The interest rate paid by the asset.
2. The expected gain or loss from changes in the exchange rate during the holding period.

To see how these are combined, let's watch a video that provides a clear numerical example and then generalizes it into a formula.

As the video demonstrates, the expected rate of return on a foreign (e.g., Euro) deposit, measured in the domestic currency (e.g., dollars), can be expressed as:

Using standard notation, if $E_{\$/€}$ is the current spot exchange rate (dollars per euro), $E_{\$/€}^e$ is the expected exchange rate in one year, and $r_{€}$ is the one-year interest rate on euro deposits, the expected dollar return on a euro deposit is:

This formula is the cornerstone of the asset market approach.

Equilibrium: The Interest Parity Condition

In an efficient global financial market, arbitrage should eliminate any differences in expected returns between assets of similar risk and liquidity. This leads to the equilibrium condition for the foreign exchange market, known as the Interest Parity Condition (IPC).

The IPC states that in equilibrium, the expected rates of return on deposits of any two currencies, measured in the same currency, must be equal.

For the dollar and euro, this means the return on a dollar deposit ($r_{\$}$) must equal the expected dollar return on a euro deposit ($R_{€}$).

This equation is the key to calculating the equilibrium exchange rate in the asset market model. It tells us that the current exchange rate, $E_{\$/€}$, must adjust until the interest rate difference between two countries ($r_{\$}-r_{€}$) is exactly offset by the expected rate of appreciation or depreciation of the foreign currency.

If $r_{\$}>R_{€}$, investors would sell euros and buy dollars, causing the dollar to appreciate (and $E_{\$/€}$ to fall) until the returns are equalized. The opposite happens if $r_{\$}<R_{€}$.

To solidify your understanding of this core concept, please watch the next segment of the video.

Calculating the Equilibrium Exchange Rate

The Interest Parity Condition gives us a powerful tool for calculation. We can rearrange the equation to solve for the current equilibrium spot exchange rate ($E_{\$/€}$).

Starting with the IPC:

Solving for the current spot rate, $E_{\$/€}$, we get:

This equation shows that the current equilibrium exchange rate is determined by three key variables: the expected future exchange rate, the domestic interest rate, and the foreign interest rate.

Practice Problem:

Let's calculate an equilibrium exchange rate. Suppose the interest rate on one-year dollar deposits is 5% ($r_{\$}=0.05$), the interest rate on one-year euro deposits is 3% ($r_{€}=0.03$), and the market expects the exchange rate to be 1.25 dollars per euro in one year ($E_{\$/€}^e=1.25$).

What is the current equilibrium spot exchange rate ($E_{\$/€}$)?

Graphical Analysis and Policy Effects

This equilibrium can also be visualized graphically, which is a powerful way to understand how policy changes affect exchange rates. The model is built on two schedules plotted against the current exchange rate (E):

1. Return on Domestic Deposits: This is a vertical line at $r_{\$}$, as it does not depend on the exchange rate.
2. Expected Return on Foreign Deposits: This is a downward-sloping curve. As the current spot rate $E_{\$/€}$ increases (the dollar depreciates), the potential for future appreciation falls, thus lowering the expected return from holding euros.

The equilibrium is at the intersection of these two schedules. The final part of the video will walk you through this graphical model and demonstrate how it responds to changes in its underlying determinants. These formal models are extensively discussed in academic literature, such as the streamlined model in the appendix of the survey by Isard (resource LINK).

This analysis leads to three crucial conclusions:

• An increase in the domestic interest rate ($r_{\$}$) makes domestic assets more attractive, causing the domestic currency to appreciate (E falls).
• An increase in the foreign interest rate ($r_{€}$) makes foreign assets more attractive, causing the domestic currency to depreciate (E rises).
• An increase in the expected future exchange rate ($E^e$) makes holding foreign currency more attractive today, causing the domestic currency to depreciate immediately (E rises).

Conclusion

In this lesson, you have moved from the accounting of international flows to the economic determination of the exchange rate. We have contrasted a simple trade-based model with the more powerful asset market approach.

Key Takeaways:

• The traditional flow model explains exchange rates through the supply and demand for currency arising from imports and exports. Equilibrium is found by setting $Q_d=Q_s$.
• The asset market model treats currencies as financial assets and is more relevant for short-run movements. It posits that investors' decisions are driven by expected rates of return.
• The equilibrium condition is the Interest Parity Condition (IPC), which states that expected returns on deposits in all currencies must be equal: $r_{\text{domestic}}=r_{\text{foreign}}+\text{Expected appreciation of foreign currency}$.
• Using the IPC, we can calculate the equilibrium spot exchange rate as a function of domestic interest rates, foreign interest rates, and expectations about the future exchange rate.
• Changes in these variables will shift the equilibrium, causing the domestic currency to appreciate or depreciate.

In our next lesson, we will close this loop by examining how a change in the exchange rate, in turn, affects a country's trade balance. This will lead us to the Marshall-Lerner condition and the famous J-curve effect, which describes the time path of the trade balance following a currency depreciation.