Given the equation for the macro model, derive the AE function, equilibrium condition and its effect on the level of equilibrium nationalincome.
This problem requires you to solve a macro model algebraically. Reading the appendix to this chapter will help you to answer this problem. But, just in case, we lead you through it step by step. The equations for the model are as follows:
i) C = a + bYn Consumption
ii) / = /q Investment (autonomous)
iii) G = G0 Government purchases
(autonomous)
iv) T = tY Net tax revenue
v) X = Xu Exports (autonomous)
vi) IM = triY Imports
a. Step 1: Recall that Yn = Y-T. Using this fact, substitute the tax function into the consumption function and derive the relationship between desiredconsumption and national income.
b. Step 2: Sum the four components of desired aggregate expenditure (C, I, G, NX). This is the aggregate expenditure {AE) function.
c. Step 3: Recall the equilibrium condition, Y = AE.Form the equation Y = AE, where AE is yourexpression for the AE function from part (b).
d. Step 4: Now collect terms and solve for Y. This isthe equilibrium value of national income.
e. Step 5: Suppose the level of autonomous expenditure, which we could call A, rises by AA. Illustrate what is the effect on the level of equilibrium nationalincome?