Question

1. You are given the following equations for the real and monetary sectors of a specific economy;

Real Sector Equations: C = 10,000 + 0.8 (Y – T); I = 20,000 – 6000 r; G = 29,000; T = 5,000 + 0.1 Y X = 10,000; M = 5,000 + 0.1 Y.

Monetary Sector Equations: Ms = 75,000; Md = 0.5 Y – 7,000 r; Yp = 200,000.

Here, C = Consumption; Y = GDP = Income; T = Taxes; I = Investment; r = interest rate; G = Govt. purchases; X = Exports; M = Imports; Ms = Money Supply; Md = Money demand.

The equilibrium condition for the real sector is: Y = C + I + G + (X – M).

The equilibrium condition for the monetary sector is Ms = Md.

Based on the given information for the economy,

(a) The real sector equilibrium equation or IS is: Y = _______________ - ___________ r.

(b) The monetary sector equilibrium equation or LM is: Y = ____________ + _________ r.

Answer 1

(a) Real Sector equilibrium equation:

At equilibrium; Y = C + I + G + X -M

=> Y = 10,000 + 0.8(Y-T) + 20,000 - 6000r + 29,000 + 10,000 - (5,000 + 0.1Y)

=> Y = 69,000 + 0.8(Y - (5000 +0.1Y)) - 6000r - 5000 - 0.1Y

=> Y = 64,000 + 0.8(Y - 5000 - 0.1Y) - 6000r - 0.1Y

=> Y = 64,000 + 0.8(0.9Y - 5000) - 6000r - 0.1Y

=> Y = 64000 + 0.72Y - 4000 - 6000r - 0.1Y

=> Y = 60,000 + 0.62Y - 6000r

=> (Y - 0.62Y) = 60,000 - 6000r

=> 0.38Y = 60,000 - 6000r

=> Y = (60,000 - 6000r)/0.38

=> Y = 157,894.74 - 15,789.47r (Real sector equilibrium equation or IS)

-------------------------------------------------------------------------------------------

(b) Monetary sector equilibrium:

At equilibrium, Ms = Md

=>

75000 = 0.5Y – 7000r

0.5Y = 75000 + 7000r

Y = (75000 + 7000r) / 0.5

Y = 150000 + 14000r (Monetary sector equilibrium equation or LM)