Answer to Question #117790 in Macroeconomics for Manan Batra

Question

Suppose government increases taxes by 100$, if MPC is 0.7 what happens to private savings, public savings, national savings and investment

Answer 1

Public saving

The effect of tax increases is that proportionately and directly leads to the increase in public savings. Thus, an increase in taxes by $100 leads to an increase in the public savings by $100.

Private saving

With regards to private saving, increase in taxes decreases the disposable income which is computed as the net difference between income and taxes (Y-T). With a marginal propensity of 0.7, the consumption level will decline with a proportion of 0.7*100 = $70. The change in private savings will thus be obtained by

Private saving = -100 – 0.7(-100) = -$30

Inference

The private savings will decline by $30.

National saving

The national saving is given as the sum total of the private savings and public savings.

National savings (NS) = Private saving + public saving

Which is given by:  NS = [Y ñT ñC(Y ñT)] + [T ñG] = Y ñC(Y ñT) ñG.

The Public savings increases proportionally with the increases in tax. Thus, an increase in tax by $100 leads to an increase in the national savings by $70. Since the tax decreases the disposable income which lowers the consumption by $70.

Investment

The national income formula is given by:

Y = C+I(r)+G+(X-M)

The national income has a direct proportional relationship with investment. Investment is an injection to the national income. The national savings is equivalent to the amount of investment and this can be seen from the equation where;

I(r) = Y – C-G-(X-M)

Since the national savings increased by $70, investments will consequently increase by the same proportion ($70). Investment is a function of real interest rates and for investment level to increase there needs to a decrease in the real interest rate. Since the tax increases leads to an increase in the national savings, the supply for the loanable funds expands (shifts) to the right leading to a fall in the equilibrium real interest rate. Ultimately, this increases the investment level.