Answer to Question #154155 in Macroeconomics for Gayathri

Question

 Suppose that initially equilibrium income was 200 units and that was also the fullemployment 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

1 To solve this , we can use the formula $Y=\frac{(1}{(1−a)}\times(C+I+G+NX)$ , where a - MPC, NX - net export

since we have consumption formula, we can write as

$Y=C' +(\frac{1}{(1−A)})\times(I+G+NX)$

when investment decline in 8 units, we count Y decline with $\frac{1}{(1−a)})\times I$

which is $\frac{1}{0.2} \times (-8) = 40$

New Y = 200-40 = $160

2 In order to make Y 200 , government has to increase spending in 40 units.

3 We can write consumption function as $C' = 25+0.8(Y-T)C ′ =25+0.8(Y−T)$

To restore 40 units with increase in consumption, we have to decrease taxes. Here is the calculation:-

$C ′ +40=25+0.8(Y−(T−x))$

$25+0.8Y−0.8T+40=25+0.8Y−0.8T+0.8x$

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

x= 50.

so we decrease tax with 50 units.