Question

Assume an economy where GDP (Q) is measured by Q= C+I+G+ (X - Im) .Assume Consumption (C) is defined by C = 800 +0.95Qd and Investment (I) is defined as I = 1500. Government Purchases (G) is given as G = 2000, Transfer payments (Tr) is given as Tr = 3300, Taxes (Tx) are given by Tx = 300 + 0.4Q Exports (X) are defined as X = 750 and Imports (Im) are defined as Im = 400 + 0.07Q

1) Calculate Autonomous Spending and the SpendingMultiplier

2) Given the answers in A, determine the equilibrium values for: Q, TX, Qd,

3) Calculate the values of C, S, Im,

4) Calculate the values of Net Exports, Government Expenditures and the Budget Deficit.

Answer 1

(1)

Autonomous spending = Autonomous consumption + I + G + X - Autonomous import = 800 + 1500 + 2000 + 750 - 400 = 4650

MPC (c) = 0.95, Tax rate (t) = 0.4, MPM (m) = 0.07

Spending multiplier = 1/[1 - c(1 - t) + m] = 1/[1 - 0.95 x (1 - 0.4) + 0.07] = 1/[(1.07 - (0.95 x 0.6)] = 1/(1.07 - 0.57) = 1/0.5 = 2

(2)

Qd = Q - Tx = Q - (300 + 0.4Q) = Q - 300 - 0.4Q = 0.6Q - 300

In equilibrium, Q = C + I + G + X - Im

Q = 800 + 0.95 x (0.6Q - 300) + 1500 + 2000 + 750 - (400 + 0.07Q)

Q = 4650 + 0.57Q - 285 - 400 - 0.07Q

(1 + 0.07 - 0.57)Q = 3965

0.5Q = 3965

Q = 7930

(3)

Tx = 300 + (0.4 x 7930) = 300 + 3172 = 3472

C = 800 + (0.95 x 3472) = 800 + 3298.4 = 4098.4

S = Q - C = 7930 - 4098.4 = 3831.6

Im = 400 + (0.07 x 7930) = 400 + 555.1 = 955.1

(4)

NX = X - Im = 750 - 955.1 = -205.1

G = 2000 (given)

Budget deficit = G - Tx = 2000 - 3472 = -1472 (a negative budget deficit of 1472 means a budget surplus of 1472).