## Related questions with answers

Suppose that the government increases taxes and government purchases by equal amounts. What happens to the interest rate and investment in response to this balanced-budget change? Explain how your answer depends on the marginal propensity to consume.

Solutions

VerifiedWe know that the demand for the economy's output (Y) depends upon three factors which are Consumption (C), Investment (I), and, Government purchases(G).

That is, Y = C $+$ I $+$ G

Further, Consumption depends upon disposable income, that is the income that remains after deduction of all taxes.

Thus, C = C(Y $-$ T), where Y is the income and T is the amount of tax imposed.

Lastly, Investment (I) depends upon the real interest rate (r). Higher the real interest rate, lower the investment and vice-versa.

We know that national saving is public saving plus private saving.

$\text{National Saving}=\left[\text{Private Saving} \right]+\left[\text{Public Saving} \right]=\left[Y-T-C\left(Y-T \right) \right]+\left[T-G \right]$

We also know that National Saving equals the Investment.

$\left[Y-T-C\left(Y-T \right) \right]+\left[T-G \right]=I\left(r \right)$

If taxes and government purchases are increased equally, $\textbf{Public Saving does not change}$.

Private saving is only affected by the tax increase therefore it will decrease by the tax increase. However consumption will decrease, which will increase the private saving. The consumption change depends on the $MPC$, the marginal propensity to consume.

The closer the $MPC$ is to $1$, the smaller the decrease in saving. The closer the $MPC$ is to $0$, the bigger the decrease in saving, however it will decrease in both cases.

Therefore, the situation will $\textbf{result in the decrease of national saving, and the increase of the real interest rate, and therefore decrease in investment}$.

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