Question

(b) 9 marks Now assume that the economy is not closed so there are imports and exports. As- sume also that there is a government in your model. Consumption is given by C = 100+ 0.8(1 – t)Y where the tax rate t = 0.25 and imports are zY where z is 0.2 and Y is income. • What is the relationship between income, consumption, investment, government expenditure, exports and imports in equilibrium? • What is the multiplier? • The government chooses to increase government expenditure by 20 without changing the tax rate. What effect does this have on income Y?

Answer 1

(b) The economy is not closed. There are imports (M) and exports (X). There is also government intervention.

Now, consumption (C) is given as

C = 100 + 0.8.(1 - t).Y.......(1)

where, tax is T = t.Y

Tax rate is given as t = 0.25

Hence, putting t = 0.25 in equation (1) we get

C = 100 + 0.8.(1 - 0.25).Y

or, C = 100 + 0.6.Y.........(2)

Government expenditure = G

Investment = I

Exports = X

Imports = M = z Y

We are given that, z = 0.2

Hence,

Import is

M = 0.2.Y........(3)

Now let's answer the following questions one by one.

• At equilibrum, Income (Y) equals the Aggrigate Expenditure (AE).

Now, Aggrigate Expenditure is

AE = C + I + G + X - M

Now, at equilibrum,

Y = C + I + G + X - M........(4)

This is the relationship between consumption, investment, government expenditure, exports and imports.

• Now, putting the values of C and M in equation (4) we get

Y = C + I + G + X - M

or, Y = 100 + 0.6.Y + I + G + X - 0.2.Y

or, (1 - 0.6 + 0.2).Y = 100 + I + G + X

or, 0.6.Y = 100 + I + G + X

Now, taking differential we get

0.6.dY = dI + dG + dX

Now, I and X are autonomous.

Hence, dI = dX = 0

Hence,

0.6.dY = dG

or, dY/dG = 1/0.6

or, dY/dG = 5/3.........(5)

The multiplier value is (5/3).

• Now, the government chooses to increase government expenditure by 20 without changing the tax rate.

Hence, dG = 20

Putting dG in equation (5) we get

dY/dG = 5/3

or, dY/20 = 5/3

or, dY = 33.3

Hence, income increases by 33.3.

Hope the solutions are clear to you my friend.