Answer to Question #95257 in Macroeconomics for komal

Question

14. Within the open-economy version of the Keynesian model, including taxes (see question 13), suppose there is an autonomous increase in imports of 20 units [ u in equation (5.25) rises by 20]. To counteract the effects of this contraction in domestic aggregate demand, assume that the government cuts taxes by 20 units. Will equilibrium income rise or fall? By how much? Explain.

Answer 1

According to open economy model,

                                                                           Y = C+I+G+NX

 

where Y is the aggregate demand of output

C is the consumption by households

I is the Investment by firms

G is the govt. expenditure

NX is the net exports, i.e. NX = X - M      

Where X is Exports and M is Imports      

C = C+ cY_d             

Assuming Consumption, Investment and government expenditure to be autonomous

Y = C+ cYd + I + G + NX

Y = C+ c(Y - T)+ I + G + NX

With change in Taxes by 20 and Imports by 20 the, and other things being unchanged, the change in income equation becomes

$\Delta$ Y = Y ₂ - Y ₁

Where Y ₂ is new aggregate output

$\Delta$ Y = - c (T ₂ - T ₁) - (M ₂ - M ₁)

$\Delta$ Y = - c( $\Delta$ T) - $\Delta$ M

$\Delta$ Y = - c (20) - 20

$\Delta$ Y = 20 ( c - 1) <= 0 0 < c <= 1

With increase in Imports and decrease in taxes, the aggregate output in the economy will decrease by 20 (c- 1) as when the consumer’s disposable income increases due to decrease in taxes, consumers increase buying domestic goods, as well as foreign goods. And also, with rise in disposable income due to taxes, consumption rises by less than the increase in income (generally when c < 1) due to marginal propensity to consume which depicts the proportion of change in consumer spending due to change in disposable income.