Open Economy Macroeconomics (Part 2) — NCERT Solutions

Open Economy Multiplier vs. Closed Economy Multiplier:

Closed Economy Multiplier:
In a closed economy (with lump-sum taxes), the multiplier is:
$$k_{\text{closed}} = \frac{1}{1 - c}$$
where $c$ = marginal propensity to consume (MPC).

Open Economy Multiplier:
In an open economy, imports $M = \bar{M} + mY$, where $m$ = marginal propensity to import (MPM). The multiplier becomes:
$$k_{\text{open}} = \frac{1}{1 - c + m}$$

Why is the open economy multiplier smaller?

Since $m > 0$, we have:
$$(1 - c + m) > (1 - c)$$

Therefore:
$$\frac{1}{1 - c + m} < \frac{1}{1 - c}$$

$$\Rightarrow k_{\text{open}} < k_{\text{closed}}$$

Economic Intuition — The Import Leakage:

The multiplier works through the income-expenditure chain: an initial increase in autonomous expenditure raises income → higher income raises consumption → higher consumption raises income further, and so on.

In an open economy, when income rises, a part of the additional income is spent on imports (foreign goods) rather than domestic goods. This spending on imports leaks out of the domestic income-expenditure circuit — it does not generate additional domestic income.

• In a closed economy: Every additional ₹1 of income leads to ₹$c$ of additional domestic spending.
• In an open economy: Every additional ₹1 of income leads to ₹$c$ of consumption, but ₹$m$ of that goes to imports, so only ₹$(c - m)$ adds to domestic demand.

This import leakage reduces the size of each round of the multiplier process, making the overall multiplier smaller.

Example: If $c = 0.8$ and $m = 0.1$:

• Closed economy multiplier $= \frac{1}{1-0.8} = 5$
• Open economy multiplier $= \frac{1}{1-0.8+0.1} = \frac{1}{0.3} \approx 3.33$

Conclusion: The open economy multiplier is smaller than the closed economy multiplier because imports act as an additional leakage from the circular flow of income, dampening the multiplier effect of any autonomous expenditure increase.

Given: Proportional taxes $T = tY$, where $t$ = tax rate.

Setting up the model:

Consumption: $C = \bar{C} + cY_D = \bar{C} + c(Y - T) = \bar{C} + c(Y - tY) = \bar{C} + c(1-t)Y$

Imports: $M = \bar{M} + mY$

Aggregate Demand for domestic goods:
$$AD = C + I + G + X - M$$
$$AD = \bar{C} + c(1-t)Y + \bar{I} + \bar{G} + \bar{X} - \bar{M} - mY$$
$$AD = \underbrace{(\bar{C} + \bar{I} + \bar{G} + \bar{X} - \bar{M})}_{A_0} + [c(1-t) - m]Y$$

Equilibrium condition: $Y = AD$
$$Y = A_0 + [c(1-t) - m]Y$$
$$Y - [c(1-t) - m]Y = A_0$$
$$Y[1 - c(1-t) + m] = A_0$$

$$\boxed{Y^* = \frac{A_0}{1 - c(1-t) + m}}$$

Open Economy Multiplier with Proportional Taxes:
$$k = \frac{\Delta Y}{\Delta A_0} = \frac{1}{1 - c(1-t) + m}$$

Comparison:

• Closed economy multiplier (lump-sum tax): $\dfrac{1}{1-c}$
• Open economy multiplier (lump-sum tax): $\dfrac{1}{1-c+m}$
• Open economy multiplier (proportional tax): $\dfrac{1}{1-c(1-t)+m}$

Why is it even smaller?
With proportional taxes, disposable income is $Y_D = (1-t)Y$. So the effective MPC out of national income is $c(1-t)$ instead of $c$. Since $c(1-t) < c$, the denominator $1 - c(1-t) + m$ is larger than $1 - c + m$, making the multiplier smaller than even the open economy multiplier with lump-sum taxes.

Conclusion: The open economy multiplier with proportional taxes is $\dfrac{1}{1 - c(1-t) + m}$, which is smaller than both the closed economy multiplier and the open economy multiplier with lump-sum taxes, because proportional taxes add another leakage to the system.

Given:
$C = 40 + 0.8Y_D$, $T = 50$, $I = 60$, $G = 40$, $X = 90$, $M = 50 + 0.05Y$

Setting up:
$Y_D = Y - T = Y - 50$
$C = 40 + 0.8(Y - 50) = 40 + 0.8Y - 40 = 0.8Y$

Aggregate Demand:
$$AD = C + I + G + X - M$$
$$AD = 0.8Y + 60 + 40 + 90 - (50 + 0.05Y)$$
$$AD = 0.8Y + 60 + 40 + 90 - 50 - 0.05Y$$
$$AD = (60 + 40 + 90 - 50) + (0.8 - 0.05)Y$$
$$AD = 140 + 0.75Y$$

(a) Equilibrium Income:

At equilibrium: $Y = AD$
$$Y = 140 + 0.75Y$$
$$Y - 0.75Y = 140$$
$$0.25Y = 140$$
$$\boxed{Y^* = 560}$$

(b) Net Export Balance at Equilibrium Income:

$$NX = X - M = 90 - (50 + 0.05 \times 560)$$
$$NX = 90 - (50 + 28)$$
$$NX = 90 - 78$$
$$\boxed{NX = 12}$$

There is a net export surplus of 12.

(c) When Government Purchases increase from 40 to 50 (i.e., $\Delta G = 10$):

New Equilibrium Income:

New $AD = 0.8Y + 60 + 50 + 90 - (50 + 0.05Y)$
$$AD = (60 + 50 + 90 - 50) + 0.75Y = 150 + 0.75Y$$

At equilibrium: $Y = 150 + 0.75Y$
$$0.25Y = 150$$
$$\boxed{Y^{**} = 600}$$

Change in equilibrium income: $\Delta Y = 600 - 560 = 40$

(This can also be verified using the multiplier: $k = \frac{1}{1-0.8+0.05} = \frac{1}{0.25} = 4$; $\Delta Y = 4 \times 10 = 40$ ✓)

New Net Export Balance:
$$NX = 90 - (50 + 0.05 \times 600) = 90 - (50 + 30) = 90 - 80 = 10$$

Change in NX: $\Delta NX = 10 - 12 = -2$

Conclusion:

• Equilibrium income increases from 560 to 600 (increase of 40).
• The net export balance worsens from 12 to 10 (decreases by 2), because higher income leads to higher imports ($\Delta M = 0.05 \times 40 = 2$).

Using the original example (before the change in G): $C = 40 + 0.8Y_D$, $T = 50$, $I = 60$, $G = 40$, $M = 50 + 0.05Y$, and now $X = 100$.

From Question 13, we know:

• $C = 0.8Y$ (after substituting $T = 50$)
• Original equilibrium: $Y^* = 560$, $NX = 12$ (with $X = 90$)

New Aggregate Demand with $X = 100$:
$$AD = 0.8Y + 60 + 40 + 100 - (50 + 0.05Y)$$
$$AD = (60 + 40 + 100 - 50) + 0.75Y$$
$$AD = 150 + 0.75Y$$

New Equilibrium Income:
$$Y = 150 + 0.75Y$$
$$0.25Y = 150$$
$$\boxed{Y^{**} = 600}$$

Change in equilibrium income:
$$\Delta Y = 600 - 560 = 40$$

(Verification using multiplier: $k = \frac{1}{0.25} = 4$; $\Delta X = 10$; $\Delta Y = 4 \times 10 = 40$ ✓)

New Net Export Balance:
$$NX = X - M = 100 - (50 + 0.05 \times 600)$$
$$NX = 100 - (50 + 30) = 100 - 80 = 20$$

Change in Net Export Balance:
$$\Delta NX = 20 - 12 = +8$$

Conclusion:

• Equilibrium income increases from 560 to 600 (an increase of 40).
• The net export balance improves from 12 to 20 (an increase of 8).

Note: Although higher income raises imports by $0.05 \times 40 = 2$, the increase in exports by 10 more than compensates, resulting in a net improvement of $10 - 2 = 8$ in the trade balance.

Given:

• Exchange rate in 2010: ₹30 = 1 dollar
• Prices in India in 2030: doubled (price level becomes $2P_{India}$)
• Prices in USA in 2030: unchanged (price level remains $P_{USA}$)

Purchasing Power Parity (PPP) Theory:

According to PPP, the exchange rate between two currencies should reflect the ratio of price levels in the two countries:
$$e = \frac{P_{\text{domestic}}}{P_{\text{foreign}}}$$

More precisely, the PPP theory states that the exchange rate adjusts proportionally to changes in relative price levels:
$$\frac{e_{2030}}{e_{2010}} = \frac{P_{\text{India, 2030}} / P_{\text{India, 2010}}}{P_{\text{USA, 2030}} / P_{\text{USA, 2010}}}$$

Calculation:

• $\frac{P_{\text{India, 2030}}}{P_{\text{India, 2010}}} = 2$ (prices doubled)
• $\frac{P_{\text{USA, 2030}}}{P_{\text{USA, 2010}}} = 1$ (prices unchanged)

$$\frac{e_{2030}}{30} = \frac{2}{1} = 2$$

$$e_{2030} = 30 \times 2 = \boxed{₹60 = 1 \text{ dollar}}$$

Conclusion: According to the Purchasing Power Parity theory, the exchange rate in 2030 will be ₹60 per dollar. Since prices in India have doubled while US prices remained unchanged, the rupee has depreciated by 50% — it now takes twice as many rupees to buy one dollar. This reflects the loss of purchasing power of the rupee due to inflation in India.

Given:

• Inflation in Country A > Inflation in Country B
• Exchange rate between A and B is fixed (does not change)

Analysis:

When inflation is higher in Country A:

• Prices of goods in Country A rise relative to prices in Country B.
• Since the exchange rate is fixed, this rise in domestic prices is not offset by any depreciation of Country A's currency.

Effect on Exports of Country A:

• Country A's goods become more expensive for buyers in Country B.
• Country B will reduce its imports from Country A (Country A's exports fall).

Effect on Imports of Country A:

• Country B's goods become relatively cheaper compared to Country A's goods.
• Country A will increase its imports from Country B.

Effect on Trade Balance of Country A:

• Exports ↓ and Imports ↑
• Country A's trade balance worsens → moves towards a trade deficit (or existing deficit widens).

Effect on Trade Balance of Country B:

• Country B's exports to A increase and imports from A decrease.
• Country B's trade balance improves → moves towards a trade surplus.

Key Point: Under a flexible exchange rate, higher inflation in Country A would cause its currency to depreciate, which would automatically restore competitiveness. But under a fixed exchange rate, this automatic adjustment does not occur, so the trade imbalance persists and worsens over time.

Conclusion: Higher inflation in Country A, combined with a fixed exchange rate, will likely cause Country A's trade balance to deteriorate (trade deficit), while Country B will experience an improvement in its trade balance (trade surplus).

Current Account Deficit — Should it be a cause for alarm?

A current account deficit means that a country is importing more goods, services, and factor incomes than it is exporting — i.e., it is spending more abroad than it earns from abroad.

When a current account deficit is NOT necessarily alarming:

1. Productive investment: If the deficit is financed by capital inflows (foreign direct investment, portfolio investment) that are being used for productive investment (building infrastructure, expanding capacity), it can lead to higher future growth and the ability to repay. Many developing countries run current account deficits as they import capital goods for development.

2. Temporary phenomenon: If the deficit is caused by a temporary shock (e.g., a bad harvest, a one-time surge in oil prices), it may correct itself over time without requiring policy intervention.

3. Sustainable financing: If the deficit is small relative to GDP and is being financed by stable long-term capital flows, it may be sustainable.

4. Reflects high growth: A fast-growing economy may attract more imports (machinery, technology) and run a current account deficit as a natural consequence of development.

When a current account deficit IS a cause for alarm:

1. Financed by debt: If the deficit is financed by short-term borrowing or depletion of foreign exchange reserves, it is unsustainable and can lead to a balance of payments crisis.

2. Large and persistent: A large, persistent deficit signals a loss of competitiveness and may lead to currency depreciation, rising debt, and loss of investor confidence.

3. Speculative attacks: A large deficit can trigger speculative attacks on the currency, forcing devaluation.

4. Consumption-driven: If the deficit reflects excessive consumption (rather than investment), it does not generate future income to repay the debt.

Conclusion: A current account deficit is not automatically a cause for alarm. Its implications depend on its size, persistence, causes, and how it is financed. A deficit that finances productive investment and is funded by stable capital inflows may be beneficial. However, a large, persistent deficit financed by short-term debt or reserve depletion is indeed a cause for concern.

Given:
$C = 100 + 0.75Y_D$, $I = 500$, $G = 750$, $T = 0.2Y$ (proportional tax, $t = 0.2$), $X = 150$, $M = 100 + 0.2Y$

Step 1: Express Consumption in terms of Y
$$Y_D = Y - T = Y - 0.2Y = 0.8Y$$
$$C = 100 + 0.75(0.8Y) = 100 + 0.6Y$$

Step 2: Set up Aggregate Demand
$$AD = C + I + G + X - M$$
$$AD = (100 + 0.6Y) + 500 + 750 + 150 - (100 + 0.2Y)$$
$$AD = (100 + 500 + 750 + 150 - 100) + (0.6 - 0.2)Y$$
$$AD = 1400 + 0.4Y$$

Step 3: Find Equilibrium Income

At equilibrium: $Y = AD$
$$Y = 1400 + 0.4Y$$
$$Y - 0.4Y = 1400$$
$$0.6Y = 1400$$
$$\boxed{Y^* = \frac{1400}{0.6} = 2333.33}$$

Step 4: Budget Deficit or Surplus

$$T = 0.2 \times 2333.33 = 466.67$$
$$G = 750$$

$$\text{Budget Balance} = T - G = 466.67 - 750 = -283.33$$

$$\boxed{\text{Budget Deficit} = 283.33}$$

(Since $T < G$, there is a budget deficit of approximately ₹283.33).

Step 5: Trade Deficit or Surplus

$$X = 150$$
$$M = 100 + 0.2 \times 2333.33 = 100 + 466.67 = 566.67$$

$$\text{Net Exports} = X - M = 150 - 566.67 = -416.67$$

$$\boxed{\text{Trade Deficit} = 416.67}$$

(Since $M > X$, there is a trade deficit of approximately ₹416.67).

Summary:

• Equilibrium Income: $Y^* \approx 2333.33$
• Budget Deficit: $\approx 283.33$ (Government expenditure exceeds tax revenue)
• Trade Deficit: $\approx 416.67$ (Imports exceed exports)

Exchange Rate Arrangements for External Stability:

Countries have adopted various exchange rate arrangements over time to manage their external accounts and bring about stability. The major arrangements are:

1. Gold Standard (Historical — pre-1930s)

• Each country fixed the value of its currency in terms of gold.
• Exchange rates between currencies were fixed through their gold parities.
• BoP adjustment occurred automatically through the price-specie-flow mechanism.
• Collapsed during the Great Depression due to its deflationary bias.

2. Bretton Woods System (1944–1971)

• Established after World War II at the Bretton Woods Conference.
• Countries fixed their exchange rates to the US dollar, and the dollar was pegged to gold at $35 per ounce.
• Countries could adjust their rates only in case of fundamental disequilibrium in BoP.
• The IMF was created to provide short-term financing to countries with BoP deficits.
• Collapsed in 1971 when the US suspended dollar-gold convertibility (Nixon Shock).

3. Flexible (Floating) Exchange Rate System

• Exchange rates are determined entirely by market forces of demand and supply.
• No government intervention; BoP adjusts automatically through exchange rate changes.
• Adopted by major economies (USA, UK, Japan, etc.) after the collapse of Bretton Woods.
• Advantage: Automatic adjustment, monetary policy independence.
• Disadvantage: Excessive volatility, uncertainty for trade and investment.

4. Managed Floating (Dirty Float)

• The current de facto system for most countries.
• Exchange rates are primarily market-determined, but central banks intervene occasionally to moderate excessive fluctuations.
• Combines flexibility with some stability.
• Official reserve transactions are non-zero.

5. Currency Boards

• A country commits to exchange its currency for a specific foreign currency at a fixed rate, backed 100% by foreign reserves.
• Example: Hong Kong's currency board pegging HK dollar to US dollar.
• Provides credibility but eliminates monetary policy independence.

6. Currency Unions / Common Currency

• A group of countries adopts a single common currency, eliminating exchange rate risk among member countries.
• Example: European Union adopting the Euro.
• Promotes trade and investment within the union but requires surrendering national monetary policy.

7. Crawling Peg

• The exchange rate is fixed but adjusted periodically in small increments in response to inflation differentials or BoP conditions.
• Provides more flexibility than a strict peg while maintaining some stability.

Conclusion: Countries choose exchange rate arrangements based on their economic size, openness, inflation history, and policy objectives. While the gold standard and Bretton Woods provided stability, they lacked flexibility. The current system of managed floating attempts to balance the benefits of both fixed and flexible systems, though no single arrangement is universally optimal.