Consider an economy described by the following equations:

y = c + i + g + nx,

y = 5,000,

g = 1,000,

t = 1,000,

c = 250 + 0.75(y – t),

i = 1,000 – 50r,

nx = 500 – 500e,

r = r* = 5.

a. in this economy, solve for national saving, investment, the trade balance, and the equilibrium exchange rate.

b. suppose now that g rises to 1,250. solve for national saving, investment, the trade balance, and the equilibrium exchange rate. explain what you find.

a. exchange rate = 1

b. exchange rate = 1.5

Explanation:

(a)  National Saving = Private saving + public saving

Private saving = Y - C - T

=> Private saving = 5000 - (250 + 0.75(Y – T)) - 1000

=> Private saving = 5000 - (250 + 0.75(5000 – 1000)) - 1000 = 750

Public saving = T - G = 1000 - 1000 = 0

National saving = 750 + 0

= 750

Investment = 1000 - 50r = 1000 - 50*5

= 750

Y = C + I + G + NX

Trade Balance = Y - C - G - I = 5000 - (250 + 0.75(5000 – 1000)) - 1000 - 750 = 0

Thus Trade Balance = 0

NX = 0 => NX = 500 – 500e = 0

=> e = 1

Thus exchange rate = 1

(b)

National Saving = Private saving + public saving

Private saving = Y - C - T

=> Private saving = 5000 - (250 + 0.75(Y – T)) - 1000

=> Private saving = 5000 - (250 + 0.75(5000 – 1000)) - 1000 = 750

Public saving = T - G = 1000 - 1250 = -250

National saving = 750 - 250

= 500

Investment = 1000 - 50r = 1000 - 50*5

= 750

Y = C + I + G + NX

Trade Balance = Y - C - G - I = 5000 - (250 + 0.75(5000 – 1000)) - 1250 - 750 = -250

Thus Trade Balance = -250

NX = -250 => NX = 500 – 500e = -250

=> e = 750/500 = 1.5

Thus exchange rate = 1.5

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