Marginal Propensity to consume (MPC) = 0.75 Proportional Tax rate = 0.20 if the government expenditure increases by Rs. 500; the rise in budget deficit will be:

Question

Accepted Answer

The correct option is 1:

The rise in the budget deficit is defined as the increase in government expenditure ($\Delta G$) minus the induced increase in tax revenue ($\Delta T$). Since tax revenue is proportional to income, $\Delta T$ depends on the change in national income ($\Delta Y$), which is generated by the initial increase in government spending through the multiplier process.

First, we must calculate the government expenditure multiplier ($k$) in an economy with proportional taxes. The formula for this multiplier is:
$$k = \frac{1}{1 - MPC(1 - t)}$$
Given Marginal Propensity to Consume (MPC) = 0.75 and proportional tax rate ($t$) = 0.20:
$$k = \frac{1}{1 - 0.75(1 - 0.20)} = \frac{1}{1 - 0.75(0.80)} = \frac{1}{1 - 0.60} = \frac{1}{0.40} = 2.5$$
Next, we determine the change in national income ($\Delta Y$) resulting from the increase in government expenditure ($\Delta G = 500$):
$$\Delta Y = k \times \Delta G = 2.5 \times 500 = 1,250$$
This increase in income generates additional tax revenue ($\Delta T$):
$$\Delta T = t \times \Delta Y = 0.20 \times 1,250 = 250$$
Finally, the rise in the budget deficit ($\Delta BD$) is the initial increase in expenditure minus the induced increase in tax revenue:
$$\Delta BD = \Delta G - \Delta T = 500 - 250 = 250$$
Therefore, the rise in the budget deficit is Rs. 250.

The incorrect option is 2 (264): This value is likely obtained by using an incorrect formula or making a mathematical error during the calculation of the multiplier or the change in income/tax revenue. If the MPC or the tax rate were slightly different, the result might be close to this figure, but it is not correct with the given parameters.

The incorrect option is 3 (248): This value is very close to the correct answer but suggests a calculation error. A value close to 250 often implies an error in rounding or a small miscalculation in the multiplier or the derived change in tax revenue, such as using a slightly wrong decimal value for $k$.

The incorrect option is 4 (260): This value would result if the induced tax revenue was calculated as Rs. 240 ($\Delta BD = 500 - 240 = 260$). This could happen if the change in income was miscalculated as 1200 instead of 1250, resulting from an error in calculating the multiplier $k$.