Question

Consider the following open economy in which the real exchange rate is fixed and equal to one. Saving, investment, government spending, taxes, imports and exports are given by:

S = −156+0.18Y

I = I and G = G (have a horizontal line at the top of two letters on the right side.)

T = T0 +0.1Y

Q = q1Y and X = X

where T0 is the level of autonomous taxes, and q1 is the marginal propensity to import. Let define the budget balance, BB, and net exports, NX, by:

BB = T−G

NX = X−Q

Assume that we know the values of I, BB and NX.

Solve for equilibrium income in terms of I, BB and NX. (Hint: you may rearrange the equilibrium condition to have in it the budget deficit and net exports)

Answer 1

In national income accounting, private saving, S = Y - T - C

So, Y - T - C = −156+0.18Y

or, Y - T₀ - 0.1Y - C = −156+0.18Y

or, 0.9Y - T₀ - C = −156+0.18Y

or, C = 156 - T₀ + 0.72Y

Now, at equilibrium,

Y = C + I + G + X - Q

or, Y = 156 - T₀ + 0.72Y + I + G + X - q₁Y

or, (1 - 0.72 + q₁)Y = 156 - T₀ + I + G + X

or, Y = (156 - T₀ + I + G + X) / (0.18 + q₁)

or, Y = (156 - T₀ - 0.1Y + 0.1Y + I + G + X - q₁Y + q₁Y) / (0.18 + q₁)

or, Y = (156 - BB + I + NX + 0.1Y + q₁Y) / (0.18 + q₁)

or, Y = (156 - BB + I + NX) / (0.18 + q₁) + (0.1 + q₁)Y / (0.18 + q₁)

or, [1 - (0.1 + q₁) / (0.18 + q₁)]Y = (156 - BB + I + NX) / (0.18 + q₁)

or, [(0.18 + q₁ - 0.1 - q₁) / (0.18 + q₁)]Y = (156 - BB + I + NX) / (0.18 + q₁)

or, [0.8/(0.18 + q₁)]Y = (156 - BB + I + NX) / (0.18 + q₁)

or, Y = (1 / 0.8)(156 - BB + I + NX)

or, Y = (5/4)(156 - BB + I + NX)

Hence the equilibrium income in terms of I, BB and NX is,

Y = (5/4)(156 - BB + I + NX)