Consider an economy with the following characteristics:

Consumption function: C = 40 + 0.9Y_D;

Planned investment:  I = 40;

Government expenditure: G = 60;

The tax function: T = 0.2Y;

Exports of the country:  X = 14

The import function: M = 10 + 0.02Y. 

Assume there are no transfer payments and no autonomous taxes.

All variables are in billions of dollars. C is consumption expenditure; Y_D is disposable income; Y is real GDP; G is government purchases of goods and services; T is taxes; I is planned investment expenditure; X is exports, and M is imports.

a. Write the aggregate expenditure function. How much is the autonomous expenditure in this economy in billions of dollars?

b. What is the equilibrium level of income of the economy?

c. Define the concept of multiplier. Calculate the size of the multiplier of the economy if exports rise from $14 billion to $30 billion.