Open Economy Macroeconomics (Part 2) — NCERT Solutions

The open economy autonomous expenditure multiplier is smaller because part of any increase in income is spent on imports.

In a closed economy, the induced increase in consumption goes only to domestic goods. But in an open economy, some of the extra consumption falls on foreign goods, so less of it raises demand for domestic output.

Therefore, imports act as an additional leakage from the circular flow, and the multiplier becomes:
$$\frac{1}{1-c+m}$$
instead of the closed economy multiplier:
$$\frac{1}{1-c}$$
Since $m>0$, the open economy multiplier is smaller.

With proportional taxes, $T=tY$, disposable income is
$$Y_D = Y - T = Y - tY = (1-t)Y$$
Consumption becomes
$$C = \bar C + c(1-t)Y$$
Equilibrium income in an open economy is
$$Y = \bar A + c(1-t)Y - mY$$
Rearranging:
$$Y - c(1-t)Y + mY = \bar A$$
$$\left[1 - c(1-t) + m\right]Y = \bar A$$
So the open economy multiplier is
$$\frac{\Delta Y}{\Delta \bar A} = \frac{1}{1 - c(1-t) + m}$$
which may also be written as
$$\frac{1}{1-c+ct+m}$$

Given:

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

Since $Y_D = Y - T$,

$$C = 40 + 0.8(Y - 50) = 40 + 0.8Y - 40 = 0.8Y$$

Equilibrium in an open economy is:

$$Y = C + I + G + X - M$$

Substitute the values:

$$Y = 0.8Y + 60 + 40 + 90 - (50 + 0.05Y)$$

$$Y = 0.8Y + 190 - 50 - 0.05Y$$

$$Y = 0.75Y + 140$$

$$Y - 0.75Y = 140$$

$$0.25Y = 140$$

$$Y = 560$$

So the equilibrium income is 560.

(b) Net export balance at equilibrium income

Net exports are:

$$NX = X - M$$

At $Y = 560$,

$$M = 50 + 0.05(560) = 50 + 28 = 78$$

So,

$$NX = 90 - 78 = 12$$

Thus, the net export balance is a surplus of 12.

(c) If government purchases increase from 40 to 50

New government spending: $G = 50$

New equilibrium condition:

$$Y = 0.8Y + 60 + 50 + 90 - (50 + 0.05Y)$$

$$Y = 0.75Y + 150$$

$$0.25Y = 150$$

$$Y = 600$$

So equilibrium income rises from 560 to 600, i.e. it increases by 40.

Now net exports at the new equilibrium income:

$$M = 50 + 0.05(600) = 50 + 30 = 80$$

$$NX = 90 - 80 = 10$$

So the net export surplus falls from 12 to 10.

Final result:

• Equilibrium income = 560
• Net exports at equilibrium = 12
• After government purchases rise to 50: equilibrium income becomes 600, and net exports become 10

From the previous example:
$$Y = 560 \text{ when } X=90$$
If exports rise to $X=100$, then autonomous demand rises by
$$\Delta X = 10$$
The multiplier from the same model is
$$\frac{1}{1-c+m} = \frac{1}{1-0.8+0.05} = \frac{1}{0.25} = 4$$
So the change in equilibrium income is
$$\Delta Y = 4 \times 10 = 40$$
New equilibrium income:
$$560 + 40 = 600$$
Net exports at the new equilibrium:
$$NX = X - M$$
At $Y=600$,
$$M = 50 + 0.05(600)=50+30=80$$
So,
$$NX = 100 - 80 = 20$$
The change in net exports from the earlier equilibrium is:

• earlier $NX = 90 - (50+0.05\times560)=90-78=12$
• new $NX = 20$

So net exports rise by
$$20-12=8$$

But if the question asks only for the net export balance, it is 20 at the new equilibrium.

By purchasing power parity (PPP), exchange rates adjust to reflect relative price levels.

Given in 2010:
$$
\text{Exchange rate} = Rs\ 30 = 1$
$$
Over 20 years:

• Prices in India double $\times 2$
• Prices in USA remain unchanged $\times 1$

So the rupee should depreciate in proportion to the rise in Indian prices:
$$30 \times \frac{2}{1} = 60$$
Therefore, according to PPP, the exchange rate in 2030 will be:
$$
Rs\ 60 = 1$
$$

If inflation is higher in country A than in country B and the exchange rate is fixed, goods in country A become relatively more expensive.

As a result:

• exports of country A tend to fall,
• imports into country A tend to rise,
• so country A’s trade balance worsens.

Therefore, country A is likely to face a trade deficit or a larger deficit in its trade balance relative to country B.

A current account deficit is not automatically a cause for alarm.

It means that a country’s payments on current account exceed its receipts. This deficit has to be financed by a capital account surplus, that is, by borrowing from abroad or by selling assets.

It becomes worrying only if the deficit is large and persistent or if the country cannot finance it sustainably. So, whether it is a cause for alarm depends on the nature and size of the deficit and whether the country can meet it through capital inflows or reserves.

Given:
$$C = 100 + 0.75Y_D,\quad I=500,\quad G=750,\quad T=0.2Y,\quad X=150,\quad M=100+0.2Y$$
Disposable income:
$$Y_D = Y-T = Y-0.2Y=0.8Y$$
Consumption:
$$C = 100 + 0.75(0.8Y)=100+0.6Y$$
Equilibrium condition:
$$Y = C+I+G+X-M$$
$$Y = (100+0.6Y)+500+750+150-(100+0.2Y)$$
$$Y = 0.6Y + 1400 - 0.2Y$$
$$Y = 0.4Y + 1400$$
$$0.6Y = 1400$$
$$Y = \frac{1400}{0.6} = 2333.33$$
So equilibrium income is 2333.33.

Budget deficit/surplus

Taxes:
$$T = 0.2Y = 0.2(2333.33)=466.67$$
Government spending is 750, so budget deficit is
$$G-T = 750 - 466.67 = 283.33$$
So there is a budget deficit of 283.33.

Trade balance

Imports:
$$M = 100 + 0.2(2333.33)=100+466.67=566.67$$
Trade balance:
$$X-M = 150-566.67 = -416.67$$
So there is a trade deficit of 416.67.

Countries have used different exchange rate arrangements to bring stability in their external accounts.

Some important arrangements are:

1. Fixed exchange rate system: The government fixes the exchange rate at a particular level and the central bank intervenes to maintain it.
2. Flexible exchange rate system: The exchange rate is determined by market demand and supply, and it adjusts automatically to BoP surpluses and deficits.
3. Managed floating / dirty floating: This is a mix of flexible and fixed systems. The exchange rate is mostly market-determined, but the central bank intervenes to reduce sharp fluctuations.
4. Devaluation and revaluation under fixed rates: Governments may officially change the fixed rate to correct external imbalances.

These arrangements are meant to promote stability in external accounts, though each has its own advantages and limitations.