Question

1. Practice with the Keynesian model algebra Suppose C = 100+ 0.6 * DI (In other words, A= 100 and MPC = 0.6); also, I = 250; X = 200; M = 100; G = 90; TR = 70; and t = 0.3. (a) Calculate equilibrium output. (b) Explain in words what would happen if output were above the level you calculated in (a). What would happen if output were below the equilibrium level? (c) Recompute equilibrium output assuming that G = 140, holding all else the same as in part (a). Now, recompute equilibrium output assuming that the tax rate t = 0.4, assuming that once again G is 90 and holding all else the same as in part (a). (d) Calculate the change in equilibrium output resulting from each of the following: (i) A rises by 30; (ii) I falls by 50 while NX rises by 40; (iii) TR rises by 60. [In each case, assume that other parameters take the values assumed in part (a). For instance, assume that G = 90 and that t= 0.3 in each case; for part (ii), assume that A is once again 100 rather than 130; and so on).

Answer 1

(a)

C = 100 + 0.6(Y + TR - T) = 100 + 0.6(Y + 70 - 0.3Y) = 100 + 0.6(0.7Y + 70) = 100 + 0.42Y + 42 = 142 + 0.42Y

Y = C + I + G + X - M

Y = 142 + 0.42Y + 250 + 90 + 200 - 100

0.58Y = 582

Y = 1003.45

(b)

(i) If output is higher than 1003.45, there will be an inflationary pressure in economy and firms will face higher demand than their current production. So they will sell out of existing inventory, reducing inventory. To meet demand, they will increase production.

(ii) If output is lower than 1003.45, there will be a recessionary pressure in economy and firms will face lower demand than their current production. So inventory will increase. Firms will decrease production.

(c)

(i) G = 140

Y = 142 + 0.42Y + 250 + 140 + 200 - 100

0.58Y = 632

Y = 1089.66

(ii) t = 0.4

C = 100 + 0.6(Y + 70 - 0.4Y) = 100 + 0.6(0.6Y + 70) = 100 + 0.36Y + 42 = 142 + 0.36Y

Y = 142 + 0.36Y + 250 + 90 + 200 - 100

0.64Y = 582

Y = 909.375

(d)

Autonomous spending multiplier = 1 / [1 - MPC(1 - t)] = 1/[1 - 0.6 x (1 - 0.3)] = 1/[1 - 0.6 x 0.7] = 1/(1 - 0.42) = 1/0.58 = 1.72

Transfer payment multiplier = MPC / [1 - MPC x (1 -t )] = 0.6 / 0.58 = 1.03

(i) When A rises by 30, Y rises by (30 x 1.72) = 51.6

(ii) Net change in autonomous spending = Rise in NX - Fall in I = 40 - 50 = - 10 (decrease)

When autonomous spending decreases by 10, Y decreases by (10 x 1.72) = 17.2

(iii) When TR rises by 60, Y rises by (60 x 1.03) = 61.8