Question

A small open economy has the following relationships among its variables: C = 50+0.75 (Y-T) I=200-20r NX = 200-50e M/P = Y-40r G = 200 T= 200 M=3.000 P= 3 r* = 4 Q1. Please calculate the following: Equilibrium Exchange Rate Net Export Income Q2. What will be the impact of increase in G by 100 on the exchange rate, income, net exports, and the money supply?

Answer 1

Part 1) We have the following information

Consumption spending: C = 50 + 0.75(Y – T) where T is taxes and Y is income

Investment: I = 200 – 20r where r is the interest rate

Net Exports: NX = 200 – 50e where e is the exchange rate

Money demand: (M/P) = Y – 40r

Government Spending: G = 200

Taxes: T = 200

Money supply: MS = 3,000

Price: P = 3

Interest rate = r = 4%

Deriving IS equation

Y = C + I + G + NX

Y= 50 + 0.75(Y – T) + 200 – 20r + 200 + 200 – 50e

Y = 650 + 0.75(Y – 200) – 20r – 50e

Y = 650 + 0.75Y – 150 – 20r – 50e

Y = 500 + 0.75Y – 20r – 50e

Y = 2000 – 80r – 200e    (IS Equation)

Deriving LM equation

Y – 40r = (MS/P)

Y – 40r = (3000/3)

Y – 40r = 1000

Y = 1000 + 40r   (LM Equation)

Equating IS and LM Equations

2000 – 80r – 200e = 1000 + 40r  

It is given that r = 4

2000 – 320 – 200e = 1000 + 160

1680 – 200e = 1160

200e = 520

Equilibrium exchange rate = 2.6

NX = 200 – 50e

NX = 200 – (50 × 2.6)

NX = 200 – 130

Equilibrium Net Exports = 70

Y = 2000 – 80r – 200e

Y = 2000 – 320 – 520

Equilibrium Income = 1160

Part 2) Now it is given that the G has increased by 100. So, now the new G is 300.

Deriving IS equation

Y = C + I + G + NX

Y= 50 + 0.75(Y – T) + 200 – 20r + 300 + 200 – 50e

Y = 750 + 0.75(Y – 200) – 20r – 50e

Y = 750 + 0.75Y – 150 – 20r – 50e

Y = 600 + 0.75Y – 20r – 50e

Y = 2400 – 80r – 200e    (IS Equation)

Deriving LM equation

Y – 40r = (MS/P)

Y – 40r = (3000/3)

Y – 40r = 1000

Y = 1000 + 40r   (LM Equation)

Equating IS and LM Equations

2400 – 80r – 200e = 1000 + 40r  

It is given that r = 4

2400 – 320 – 200e = 1000 + 160

2080 – 200e = 1160

200e = 920

Equilibrium exchange rate = 4.6

NX = 200 – 50e

NX = 200 – (50 × 4.6)

NX = 200 – 230

Equilibrium Net Exports = – 30

Y = 2400 – 80r – 200e

Y = 2400 – 320 – 920

Equilibrium Income = 1160

So, we can see that the increase in the government spending results in the appreciation of the currency leading to negative net exports and unchanged equilibrium income. In other words, the stimulation provided by the increased government spending has been completely negated by the decline in net exports due to the appreciation of the exchange rate.