Answer to Question #42659 in Macroeconomics for Amaar

Question

Consider an economy with the following characteristics (all variables measured in
billions of US DOLLAR
· The households behave such that the consumption function is:
· C = 5 + 0.8 (Y-T), where Y- T = disposable income and T = Tax.
· The government spending (G) = 7 and Tax (T) = 0.2Y.
· The business sector investment is: I = 6,
· Exports (E) = 4 and Import (M) = 2 + 0.14Y
a) Find the equilibrium expenditure
b) Suppose that the government increases its purchases of goods and services by 2 billion$
i) What is the new equilibrium expenditure?
ii) What is the multiplier value?

Answer 1

We can write an equation:

Y= C + I + G + NE, where

C- Consumer spending is a personal consumer expenditures for all citizens that includes the costs of durable goods and the current consumption and the services. This is an expense for food, clothing, housing, cultural products, household products etc.
I - Investment costs cover the basic types of private investment in production by firms and entrepreneurs. These costs are used for the ultimate purchase of machinery and equipment, industrial buildings, the
increase in reserves of inputs, housing etc.
G - The government spending is government purchases of goods and services. This group includes the costs of federal, national and local government purchases of the companies’ final product for public use. The government spending does not include transfer payments.
NE - Net exports show how foreign spending on goods and services produced in the country exceed the country costs for the purchase of goods and services produced in other countries.

So,
Y= 5 + 0.8 (Y-T) + 6 + 7 + (4 – (2 + 0.14Y)) = 5 + 0.8 (Y-0.2Y) + 6 + 7 +(4 – 2 - 0.14Y) = 5 + 0.64Y + 6 + 7 + 2 - 0.14Y = =20 + 0.5Y
0.5Y= 20
Y = 40

If the government increases its purchases of goods and services by $2 billion
Y = 5+ 0.8 (Y-T) + 6 + 9 + (4 – (2 + 0.14Y)) = 5 + 0.64Y + 15 + 2 - 0.14Y = 22 +0.5Y
0.5Y= 22
Y= 44

So,the increase Y is 4 (44 – 40 = 4)

The formula for consumption function is:
C= Co + c’ (Y-T), where c’ is the marginal propensity to consume
C= 5 + 0.8 (Y-T)

So, the marginal propensity to consume is 0.8
We can find a multiplier value using the following formula:
Multiplier= 1 / (1 - MPC) = 1/(1-0.8) = 5