Question

7. Consider the following income-expenditure model of a closed economy. The aggregate consumption function is C = 100 +0.8(Y – T); taxes are T = 380; investment, I, is 300 and government expenditure, G, is 200.

(a) Calculate the multiplier, equilibrium income and the government budget surplus [6 marks]

(b) Now let taxes, T = 10 + 0.25Y. Recalculate the multiplier, equilibrium income and the government budget surplus. Try to explain any differences between your answers and your answers to part (a). [10 marks]

(c) Now we further extend the model and open the economy to trade. Let net exports be NX = 444 - 0.3Y. Keep the tax function as in (b). Recalculate the multiplier and equilibrium income and again explain any differences between your answers and those in part (b).

Answer 1

(a)

(I) Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1/0.2 = 5

(II) In equilibrium, Y = C + I + G

Y = 100 + 0.8(Y - 380) + 300 + 200

Y = 600 + 0.8Y - 304

0.2Y = 296

Y = 1480

(III) Budget surplus = T - G = 380 - 200 = 180

(b)

(I) Multiplier = 1 / [1 - MPC x (1 - t)] = 1 / [1 - 0.8 x (1 - 0.25)] = 1/[1 - (0.8 x 0.75)] = 1/(1 - 0.6) = 1/0.4 = 2.5

(II) In equilibrium, Y = C + I + G

Y = 100 + 0.8[Y - 10 - 0.25Y] + 300 + 200

Y = 600 + 0.8(0.75Y - 10)

Y = 600 + 0.6Y - 8

0.4Y = 592

Y = 1480

(III) Budget surplus = 10 + (0.25 x 1480) - 200 = 370 - 190 = 180

Since the sump-sum tax is equivalent to the per-unit tax, equilibrium income is the same. Therefore budget surplus is also the same.

(c)

(I) Multiplier = 1 / [1 - MPC x (1 - t) + MPM] = 1/[1 - 0.8 x (1 - 0.25) + 0.3] = 1/[1 - 0.6 + 0.3] = 1/0.7 = 1.43

(II) In equilibrium, Y = C + I + G + NX

Y = 100 + 0.8[Y - 10 - 0.25Y] + 300 + 200 + 444 - 0.3Y

Y = 1044 + 0.6Y - 8 - 0.3Y

0.7Y = 1036

Y = 1480

(III) Budget surplus = 10 + (0.25 x 1480) - 200 = 370 - 190 = 180

In this case, value of exports equal the value of import when equilibrium income is obtained. Therefore equilibrium income and budget surplus are also the same.