Answer to Question #153805 in Macroeconomics for Sandali

Question

Suppose that initially equilibrium income was 200 units and that was also the full￾employment level of income. Assume that the consumption function is

C = 25 + 0.8YD

And that, from this initial equilibrium level, we now have a decline in investment of 8  units. What will be the new equilibrium level of income? What increase in government  spending would be required to restore income to the initial level of 200? Alternatively,  what reduction in tax collections would be sufficient to restore an income level of 200?

Answer 1

Solution:

1. We use a formula $Y = (\tfrac{1}{(1-a)})*(C+I+G+NX)$, where a - MPC, NX - net export. But since we have a formula for consumption we can write this: $Y = C'+(\frac{1}{(1-A)})*(I+G+NX)$

So if Investment declines in 8 units we count that Y declines with$(\tfrac{1}{(1-a)})*I'$ which is $\tfrac{1}{0.2}*(-8)=40$. 

A new level of income equilibrium is 360.

2. In order to make Y 200 again the government has to increase spendings by 40 units as well.

3. Consumption function we can write as $C' = 25+0.8(Y-T)$ . To restore 40 units gap with the increase of consumption we have to decrease taxes. We can calculate it like this:

$C'+40=25+0.8(Y-(T-x))$

$25+0.8Y-0.8T+40 = 25+0.8Y-0.8T+0.8x$

$x=\tfrac{40}{0.8}$

$x=50$

Answer:

We have to decrease taxes by 50 units.