AP Macroeconomics

## Learning Outcomes

- Derive the open-economy saving-investment identity from the GDP formula
- Distinguish between the closed-economy identity **S = I** and the open-economy identity **S = I + NCO**
- Explain what **S - I** means and how its sign links to trade surpluses and trade deficits
- Identify how national saving, domestic investment, and net capital outflow fit into the loanable funds market
- Explain how the real interest rate affects **NCO**, the foreign exchange market, and the value of a currency
- Apply these ideas in AP-style calculations and chain-reasoning questions

## AP Macroeconomics Syllabus

For the AP Macroeconomics, you are expected to understand the open-economy investment identity, with a focus on the following syllabus points:

- Know the identity **S = I + NCO**
- Derive the identity from **Y = C + I + G + NX** and **S = Y - C - G**
- Understand that **NCO = NX** in the AP model
- Identify **national saving** as the supply of loanable funds
- Explain that in an open economy, demand for loanable funds includes **domestic investment and net capital outflow**
- Understand how a higher real interest rate reduces **NCO**
- Explain the chain: higher real interest rate -> lower NCO -> lower supply of domestic currency in foreign exchange -> appreciation -> lower net exports
- Distinguish a country with **S > I** from one with **S < I**

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. How do you derive **S = I + NCO** from the open-economy GDP identity?
2. What does **S - I** tell you about a country's relationship with the rest of the world?
3. Why is **NCO** part of demand in the loanable funds market?
4. If the real interest rate rises, what happens to **NCO**, the supply of domestic currency in foreign exchange, and net exports?
5. What does it mean if a country has **S < I**?

## Introduction

In a closed economy, students often learn the simple identity **saving equals investment**. That works only when there is no trade and no international financial flow. In an open economy, some national saving finances investment at home, but some may be used to buy foreign assets. That is why the AP course uses a wider identity: **S = I + NCO**.

This matters because AP questions often connect three ideas at once: the loanable funds market, international capital flows, and the foreign exchange market. If you only memorize the formula without seeing how the parts fit together, you will struggle with multi-step questions. If you understand the logic, many FRQs become much easier.

> **Key Term: open economy**
> An economy that trades goods, services, and financial assets with other countries.

### Deriving the open economy investment identity

Start with the open-economy GDP identity:

$$
Y = C + I + G + NX
$$

This says total output or income (**Y**) equals consumption, investment, government purchases, and net exports.

Now subtract **C** and **G** from both sides:

$$
Y - C - G = I + NX
$$

The left side, **Y - C - G**, is **national saving**.

> **Key Term: national saving**
> The portion of national income not used for consumption or government purchases; **S = Y - C - G**.

So we can rewrite the equation as:

$$
S = I + NX
$$

In the AP open-economy model, **net exports equal net capital outflow**:

$$
NX = NCO
$$

Substitute that into the equation:

$$
S = I + NCO
$$

That is the open-economy investment identity.

> **Key Term: net capital outflow (NCO)**
> The purchase of foreign assets by domestic residents minus the purchase of domestic assets by foreigners.

Why does **NX = NCO**? Because international trade flows and international financial flows are two sides of the same transaction. If a country exports more than it imports, it receives more from abroad than it spends abroad. Those funds must go somewhere, and in the AP model they show up as net purchases of foreign assets. If a country imports more than it exports, it must be financed by funds coming in from abroad.

This gives two useful rearrangements:

$$
S - I = NCO
$$

and because **NCO = NX**,

$$
S - I = NX
$$

These versions are often easier to interpret than **S = I + NCO**.

> **Test Tip:** If an FRQ asks you to "show" or "derive" the identity, begin with **Y = C + I + G + NX**, subtract **C** and **G**, define **S**, then replace **NX** with **NCO**. Write each algebra step clearly.

A common mistake is to jump straight to **S = I + NCO** without showing where it came from. On AP FRQs, the reasoning step matters.

### What S - I tells you in an open economy

The expression **S - I** tells you whether a country is a net lender or a net borrower in world financial markets.

If:

$$
S > I
$$

then:

$$
S - I > 0
$$

so:

$$
NCO > 0
$$

and therefore:

$$
NX > 0
$$

That means the country saves more than it invests domestically. The extra saving flows abroad to buy foreign assets. The country is a **net lender** to the rest of the world and has a **trade surplus**.

> **Key Term: trade surplus**
> A situation in which exports exceed imports, so **NX > 0**.

If instead:

$$
S < I
$$

then:

$$
S - I < 0
$$

so:

$$
NCO < 0
$$

and:

$$
NX < 0
$$

Now domestic investment is larger than national saving. The country must rely on foreign funds to help finance that investment. It is a **net borrower** from the rest of the world and has a **trade deficit**.

> **Key Term: trade deficit**
> A situation in which imports exceed exports, so **NX < 0**.

This is one of the most tested interpretations in open-economy macro. Do not treat **negative NCO** as "impossible." It simply means foreigners are buying more domestic assets than domestic residents are buying foreign assets.

Worked example:

Suppose a country has:

- **Y = 5,000**
- **C = 3,200**
- **G = 900**
- **I = 700**

Step 1: Find national saving

$$
S = Y - C - G
$$

$$
S = 5000 - 3200 - 900 = 900
$$

Step 2: Find **NCO**

$$
S = I + NCO
$$

$$
900 = 700 + NCO
$$

$$
NCO = 200
$$

Step 3: Interpret

Because **NCO = 200**, the country has positive net capital outflow. Since **NCO = NX**, net exports are also **200**, so the country has a trade surplus.

Now change only investment to **I = 1,100**.

$$
900 = 1100 + NCO
$$

$$
NCO = -200
$$

That means the country has negative net capital outflow and a trade deficit of **200**.

> **Test Tip:** On MCQs, once you compute **S** and compare it with **I**, you can often infer **NCO**, **NX**, and whether the country is a net lender or borrower without doing any extra graphing.

### The loanable funds market in an open economy

In the loanable funds market, the vertical axis is the **real interest rate** and the horizontal axis is the quantity of loanable funds.

> **Key Term: real interest rate**
> The nominal interest rate minus inflation; the inflation-adjusted cost of borrowing and reward for lending.

In an open economy:

- **Supply of loanable funds = national saving**
- **Demand for loanable funds = domestic investment + NCO**

Students often understand why domestic investment demands funds. Firms borrow to build factories, buy machines, or fund new projects. But why is **NCO** also part of demand?

Because when domestic residents buy foreign assets, they need funds to do so. Buying a bond issued abroad or purchasing stock in another country uses part of the nation's saving. So saving has two uses:

- financing domestic investment
- financing net purchases of foreign assets

That is exactly what **S = I + NCO** means in market language.

A second key point is that **NCO is inversely related to the real interest rate**. If domestic real interest rates rise, domestic financial assets become more attractive relative to foreign assets. Domestic residents send less money abroad, so **NCO falls**.

This gives the AP chain:

- real interest rate rises
- **NCO falls**
- fewer domestic funds flow abroad

If the real interest rate falls, the reverse happens:

- domestic assets are relatively less attractive
- residents buy more foreign assets
- **NCO rises**

This matters because the real interest rate set in the loanable funds market helps determine international capital flows.

A budget deficit is a standard AP application. Recall:

- **private saving = Y - T - C**
- **public saving = T - G**
- **national saving = private saving + public saving**
  > **Key Term: public saving**
  > Government tax revenue minus government spending, **T - G**.

If the government runs a larger budget deficit, then **T - G** falls, so public saving falls. That reduces national saving, which shifts the supply of loanable funds left. The real interest rate rises. Then domestic investment and/or NCO are crowded out.

This is why open-economy crowding out can reduce not just domestic investment, but also net capital outflow and net exports.

### Linking loanable funds to foreign exchange and net exports

The open-economy model becomes more powerful when you connect the loanable funds market to the foreign exchange market.

In the foreign exchange market, **NCO supplies domestic currency**. Why? Because when domestic residents buy foreign assets, they must exchange domestic currency for foreign currency. That action puts domestic currency into the foreign exchange market.

So:

- **NCO = supply of domestic currency in foreign exchange**

In the AP model, the real interest rate from the loanable funds market determines **NCO**, and that **NCO** becomes the supply of currency in foreign exchange.

Now follow the full chain:

1. National saving falls, perhaps because of a budget deficit.
2. Supply of loanable funds shifts left.
3. Real interest rate rises.
4. Higher real interest rate reduces **NCO**.
5. Lower **NCO** means less domestic currency supplied in foreign exchange.
6. The domestic currency appreciates.
7. Appreciation makes exports less competitive and imports cheaper.
8. **NX falls**.

That is a classic AP FRQ sequence.

The reverse also matters:

1. National saving rises.
2. Supply of loanable funds shifts right.
3. Real interest rate falls.
4. **NCO rises**.
5. More domestic currency is supplied in foreign exchange.
6. Currency depreciates.
7. Depreciation raises net exports.
8. **NX rises**.

Worked example of the chain:

Suppose Congress increases the budget deficit.

- Public saving falls because **T - G** decreases.
- National saving falls.
- In the loanable funds market, supply shifts left.
- The equilibrium real interest rate rises.
- Because **NCO** is inversely related to the real interest rate, **NCO** falls.
- In the foreign exchange market, the supply of domestic currency falls.
- The domestic currency appreciates.
- With appreciation, exports fall and imports rise.
- Net exports fall.

This is one of the best examples of how a domestic fiscal change affects international trade.

A common confusion is sign language. In AP terms:

- **NCO positive** means net capital outflow
- **NCO negative** means net capital inflow from abroad, even if AP still writes the identity with NCO

So if a question uses **capital inflow**, remember it moves opposite to **NCO**.

Another confusion is mixing up the balance of payments capital and financial account with **NCO**. In AP sign convention, they move in opposite directions. If **NCO** is positive, the capital and financial account tends to be negative, and vice versa.

> **Test Tip:** For graph questions, label the loanable funds market with **real interest rate** on the vertical axis and **quantity of loanable funds** on the horizontal axis. Do not use nominal interest rate there. That mistake costs points.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- In an open economy, the key identity is **S = I + NCO**
- The identity can be derived from **Y = C + I + G + NX** and **S = Y - C - G**
- In the AP model, **NCO = NX**
- Rearrangements include **S - I = NCO** and **S - I = NX**
- National saving is the supply of loanable funds
- In an open economy, demand for loanable funds includes **domestic investment and NCO**
- If **S > I**, then **NCO > 0** and **NX > 0**, giving a trade surplus
- If **S < I**, then **NCO < 0** and **NX < 0**, giving a trade deficit
- A higher real interest rate reduces **NCO**
- **NCO** supplies domestic currency in the foreign exchange market
- Lower national saving raises the real interest rate and can reduce **NCO** and **NX**
- Budget deficits reduce public saving and can crowd out domestic investment and/or net capital outflow

## Key Terms and Concepts

- open economy
- national saving
- net capital outflow (NCO)
- trade surplus
- trade deficit
- real interest rate
- public saving


The Loanable Funds Market - Open economy investment identity