Question 3.16: In a two-sector economy, autonomous consumption expenditure,......

(a) (i) Step 1: Households’ consumption expenditure and firms’ investment expenditure are the only components of aggregate expenditure, therefore

E = C + I = C_0 + bY + I_0 = 50 + 0.5Y + 100 = 150 + 0.5Y

Step 2: At equilibrium, Y = E (equation 3.25), therefore:

The equilibrium level of national income Y_e = 300.

(ii) When the equilibrium level of income has been found, the equilibrium level of consumption is calculated directly from the consumption function,

 C_e = C_0 + bY_e
= 50 + 0.5(300) = 50 + 150 = 200                                    (3.29)

(b) The consumption function C = 50 + 0.5Y, the expenditure function E = 150 + 0.5Y and the equilibrium condition Y = E are plotted in Figure 3.15, with E plotted vertically and Y plotted horizontally. The equilibrium condition, Y = E, is represented by a 45° line from the origin, provided the number scale is the same on both axes. Graphically, equilibrium national income Y_e is illustrated in Figure 3.15(a) with the equilibrium point occurring at the point of intersection of the expenditure equation and the line Y = E. The point of intersection is at Y = 300 = E. Graphically, the equilibrium level of consumption, C_e, is at the point of intersection of the consumption function and the vertical line Y_e = 300.

(c) Since C_e = 200, the equilibrium level of savings S_e = Y_e  –  C_e = 300 – 200 = 100. The savings function S = Y − (C_0 + bY) = –C_0 + (1 – b)Y = –50 + 0.5Y is plotted in Figure 3.15(b). Graphically, investment expenditure is illustrated by a horizontal line in Figure 3.15(b). Notice that, at equilibrium national income, savings is equal to investment,

S_e = I

Therefore, in this example, one can also say that equilibrium national income occurs when savings (leakages) are equal to investment (injections).