Government Budget and the Economy

Public goods must be provided by the government because the market mechanism cannot supply them efficiently.

- They are non-rivalrous: one person's consumption does not reduce what is available to others.
- They are non-excludable: it is not feasible to exclude anyone from enjoying their benefits.
- Because users can enjoy them without paying, free-rider problems arise.
- Therefore, private firms will not voluntarily provide them, and the government must step in through public provision financed by the budget.

Examples include national defence, roads, government administration, and measures to reduce air pollution.

Revenue expenditure is expenditure incurred for purposes other than the creation of physical or financial assets of the central government. It includes:
- normal functioning of government departments and services,
- interest payments on debt,
- grants to state governments and other parties.

Capital expenditure is expenditure that results in:
- creation of physical assets or financial assets, or
- reduction in financial liabilities.

It includes expenditure on land, buildings, machinery, equipment, investment in shares, and loans and advances to state/UT governments, PSUs and others.

So, the main difference is that revenue expenditure does not create assets, while capital expenditure does.

The statement is correct because fiscal deficit measures the government's total borrowing requirement.

By definition:

$$\text{Gross fiscal deficit} = \text{Total expenditure} - (\text{Revenue receipts} + \text{Non-debt creating capital receipts})$$

This means fiscal deficit is the part of expenditure not met by current revenue and non-debt capital receipts. Therefore, it has to be financed by borrowing.

The chapter states that fiscal deficit is financed through:
- net borrowing at home,
- borrowing from RBI,
- borrowing from abroad.

So, fiscal deficit shows how much the government must borrow from all sources to meet its spending needs. A larger fiscal deficit means a larger borrowing requirement.

The relationship is:

$$\text{Revenue deficit} = \text{Revenue expenditure} - \text{Revenue receipts}$$

and

$$\text{Fiscal deficit} = \text{Total expenditure} - (\text{Revenue receipts} + \text{Non-debt creating capital receipts})$$

Since total expenditure includes revenue expenditure and capital expenditure, revenue deficit is a part of fiscal deficit.

Also, the chapter gives:

$$\text{Fiscal deficit} = \text{Revenue deficit} + \text{Capital expenditure} - \text{Non-debt creating capital receipts}$$

So, if revenue deficit is large, it tends to raise fiscal deficit and indicates that more borrowing is being used for current spending rather than investment.

Given:
- $I = 200$
- $G = 150$
- Net taxes $= T - TR = 100$
- $C = 100 + 0.75Y$

Since net taxes are given, disposable income is:

$$YD = Y - 100$$

So consumption becomes:

$$C = 100 + 0.75(Y - 100) = 100 + 0.75Y - 75 = 25 + 0.75Y$$

### (a) Equilibrium income
Equilibrium condition:

$$Y = C + I + G$$

Substitute values:

$$Y = (25 + 0.75Y) + 200 + 150$$

$$Y = 375 + 0.75Y$$

$$Y - 0.75Y = 375$$

$$0.25Y = 375$$

$$Y = 1500$$

But this uses the consumption function after deducting net taxes incorrectly if net taxes are already meant to be directly used in aggregate demand. The standard textbook treatment for this kind of question is to use the autonomous expenditure with net taxes as a reduction in disposable income, so the correct equilibrium is:

$$Y = \frac{1}{1-c}(\bar C - cT + I + G)$$

Here, the autonomous part is:

$$\bar C - cT + I + G = 100 - 0.75(100) + 200 + 150 = 100 - 75 + 350 = 375$$

Thus:

$$Y = \frac{1}{1-0.75} \times 375 = 4 \times 375 = 1500$$

So the equilibrium income is **$1500$**.

### (b) Multipliers
Government expenditure multiplier:

$$\frac{1}{1-c} = \frac{1}{1-0.75} = \frac{1}{0.25} = 4$$

Tax multiplier:

$$\frac{-c}{1-c} = \frac{-0.75}{0.25} = -3$$

### (c) If government expenditure increases by 200

$$\Delta Y = \frac{1}{1-c}\Delta G = 4 \times 200 = 800$$

So equilibrium income rises by **$800$**.

Given:
- $C = 20 + 0.80Y$ with lump-sum taxes and transfers,
- $I = 30$, $G = 50$, $TR = 100$.

Disposable income:

$$YD = Y - T + TR$$

From the chapter's setup, with lump-sum taxes not separately given in part (a), the autonomous expenditure is:

$$\bar A = \bar C + c\bar{TR} + I + G = 20 + 0.8(100) + 30 + 50$$

$$\bar A = 20 + 80 + 30 + 50 = 180$$

Then equilibrium income is:

$$Y = \frac{1}{1-c}\bar A = \frac{1}{1-0.8}\times 180 = 5 \times 180 = 900$$

However, the question as printed in the chapter intends the standard formula with lump-sum taxes omitted in the given data, so the textbook exercise typically takes the equilibrium from the autonomous expenditure listed. But because the question includes $TR=100$, the only way to solve it from the given information is:

$$Y = \frac{1}{1-0.8}(20 + 30 + 50 + 0.8\cdot 100) = 900$$

### Multiplier

$$\frac{1}{1-c} = \frac{1}{1-0.80} = 5$$

### (b) If government expenditure increases by 30

$$\Delta Y = 5 \times 30 = 150$$

### (c) If a lump-sum tax of 30 is added to pay for the increase in government purchases
Balanced budget change means:

$$\Delta Y = \Delta G + \left(\frac{-c}{1-c}\right)\Delta T$$

With $c=0.8$ and $\Delta G = \Delta T = 30$:

$$\Delta Y = 5(30) - 4(30) = 150 - 120 = 30$$

So equilibrium income rises by 30.

Note: If one uses only the chapter's balanced budget multiplier result, the change would be equal to the increase in government spending, but that applies when the increase in spending is financed by an equal tax increase in the model with autonomous taxes as used in Box 5.1. The intended textbook result is 30? Actually, from the chapter, balanced budget multiplier = 1, so an increase in $G$ by 30 financed by a 30 increase in taxes changes income by 30. Hence the final effect is **+$30$**.

From the previous question, $c = 0.80$.

### Effect of a 10 per cent increase in transfers
Transfers are $100$, so a 10% increase is:

$$\Delta TR = 10$$

Transfer multiplier:

$$\frac{c}{1-c} = \frac{0.8}{0.2} = 4$$

So:

$$\Delta Y = 4 \times 10 = 40$$

### Effect of a 10 per cent increase in lump-sum taxes
A 10% increase in lump-sum taxes means:

$$\Delta T = 10$$

Tax multiplier:

$$\frac{-c}{1-c} = \frac{-0.8}{0.2} = -4$$

So:

$$\Delta Y = -4 \times 10 = -40$$

### Comparison
- Transfers raise output by 40.
- Taxes reduce output by 40.

Thus, a transfer increase and an equal tax increase have equal absolute effects but opposite directions. If the question intends a 10% change of the given value $TR=100$, then the answer above follows directly.

Given:
- $C = 70 + 0.70Y$
- $I = 90$
- $G = 100$
- $T = 0.10Y$

### (a) Equilibrium income
Disposable income is:

$$YD = Y - T = Y - 0.10Y = 0.90Y$$

Consumption becomes:

$$C = 70 + 0.70(0.90Y) = 70 + 0.63Y$$

Equilibrium condition:

$$Y = C + I + G$$

$$Y = 70 + 0.63Y + 90 + 100$$

$$Y = 260 + 0.63Y$$

$$Y - 0.63Y = 260$$

$$0.37Y = 260$$

$$Y = \frac{260}{0.37} \approx 702.70$$

So equilibrium income is approximately **$702.7$**.

### (b) Tax revenues at equilibrium income

$$T = 0.10Y = 0.10 \times 702.70 \approx 70.27$$

Since government purchases are $100$ and tax revenue is only about $70.27$, the government does not have a balanced budget.