Question

(a) What is the equation for the aggregate expenditure function (AE)?

(b) Determine the Equilibrium level of Output (Income) for this economy

(c) If Investment (I) increases by $200 million, determine the new equilibrium level of Output (Income). Please show your work.

Answer 1

Aggregate Expenditure has five Components:

Consumsumption, Investment, Government Expenditure, Exports and Imports

a. AE= C+I+G+NX, where NX is the net exports which equals (exports-imports)

In equilibrium. AE=Y

Y= C+I+G+NX

b. Y= cY+I_bar+ iY+G+NX, where c is the marginal propensity to consume and cY is the part of Income which is consumed, I_bar is the autonomous investment independent of the level of income, i is the proportion of the Income Invested and iY is the induced Investment

(1-c-i)Y=I_bar+G+NX

Y=[I_bar+G+NX] / (1-c-i); I_bar,G,NX are all autonomous, idependent of the level of investment

Note: In general models entire Investment is autonomous sometimes, which makes i = 0 & Y= [I+G+NX]/ (1-c)

c. Here entire Investment is autonomous, since induced investment function not mentioned. Therefore, if autonomous Investment I, increases by 200 other factors remaining constant:

dY=dI/(1-c)

Thus, Y increases by the value of 200/(1-c), and there is a shift of equilibrium rightwards. Y curve is a 45 degree line which is equidistant from X and Y axis. Since c does not channge, slope of the AE function remains same, change in autonomous component makes the intercept increase. Value of Income in the economy increases from Y1 (initial income) to Y2.

Thus, new Income Y2= [ (I+200)+G+NX]/ (1-c), where I is the initial autonomous investment