Answer to Question #154335 in Macroeconomics for Sandeepa Jans

Question

Suppose that government spending was increased by 15 million and that this increase was financed by a 15 million increase in taxes. Would equilibrium income change or remain the same as a result of these two policy actions and why is it important? If equilibrium income changed, in which direction would it move, and by how much? Explain.

Answer 1

$\bold {Summary \space Answer}$

Increasing government spending and taxation by an equal amount, $15 million, will result in equilibrium income increasing by the same amount: by $15 million. This is because the balanced-budget multiplier is equal to 1.

This policy is important because the government budget remains unaffected, that is, the government do not suffer a budget deficit, and neither do it realise a surplus.

$\bold {Explanation}$

The impact on equilibrium national income of increasing government spending, G, and taxation, T, by the same amount is explained by the balanced-budget multiplier. The balanced-budget multiplier is the sum of the expenditure multiplier and the tax multiplier. This multiplier is always equal to 1.

In this case, let us assume that the marginal propensity to consume is 0.8, that is, MPC = 0.8.

The government spending multiplier is given by: $G_{k} = \dfrac {1}{1-MPC}$

$= \dfrac {1}{1-0.8}$

$= \dfrac {1}{0.2}$

$\bold {= 5}$

$G_{k}$ is positive because an increase in G increase GDP, and vice-vesa. Thus, the two are positively related.

As a result, following an increase in G by $15 million, equilibrium national income will increase 5 times the increase in G, by:

$∆Y_{e} = \$15m × 5$

$\bold {=\$75 \space million}$

Also, the tax multiplier is given by:

$T_{k} = -\dfrac {MPC}{1-MPC}$

$= - \dfrac {0.8}{1-0.8}$

$= -\dfrac {0.8}{0.2}$

$\bold {=-4}$

The tax multiplier is negative because taxation and GDP are negatively related - an increase in taxation lowers GDP, and vice-versa.

Correspondingly, following an increase in taxation by $15 million, equilibrium national income will decrease 4 times the increase in taxation, by:

$∆Y_{e} = \$15m × (-4)$

$\bold {=-\$60 \space million}$

Finally, the net change in equilibrium national income is the sum total of the above changes, that is:

$∆Y_{e} = \$75m +(-\$60m)$

$\bold {=\$15 \space million \space increase}$

$\bold {Alternatively}$

The balanced-budget multiplier is given by: $k = G_k + T_k$

$= 5+(-4)$

$\bold {=1}$

Hence, $∆Y_e = \$15m × 1$

$\bold {=\$15 \space million \space increase}$

It is important to note that these results are always true whatever the value of MPC.

These policies, increase G and T by equal amounts, are vital in the sense that the fiscal budget remains in its position. There is a $0 net effect on the fiscal budget since $G - T = \$15m - \$15m$

$= \$0$

Thus, equilibrium national income increases without inviting fiscal deficit.

$\bold {Reference}$

https://courses.byui.edu/econ_151/presentations/lesson_07.htm