Question

Consider the following:

? = 300 + 0.7???0 = 150
?0 = 450
? = 0.2 × ?

?0 = 40
?? = 0.15×?

? is the consumption, ?0 is the autonomous investment expenditure, ?0 is the autonomous government’s expenditure, T is the tax, ?0 is the autonomous export, and ?? is the import.

1. a) Calculate the equilibrium income (GDP). Show your calculations.

2. b) Find the value of the multiplier. Show your calculations.

3. c) Calculate the budget balance of the government and draw it on a graph.

4. d) If consumer confidence (autonomous consumption) drops from 300 to 250, find the new

   value of Y. Show your calculations.

5. e) Describe the automatic stabilizer process in which the economy would recover from the

   shock in (d) in the long-run. Show the process in AS/AD model and explain.

Answer 1

a. GDP = Consumption+ Invetsmnet +Govenrment expenditure+ Net exports where net exports= Exports-Imports

Thus, Y= 300+0.7Yd+150+450+(40-0.15Y) where Yd is disposable income and is equal to Y-T where T is taxes

Thus, Y= 300+0.7(Y-0.2Y)+150+450+(40-0.15Y)

Y=940+.56Y-0.15Y

Y-.41Y=940

0.59Y=940

Y=940/0.59=1593.22

b. Multiplier= 1/(1-MPC) where MPC is given in the consumption function as C= c0+(MPC)Yd

Multiplier= 1/(1-0.7)=1/0.3=3.33

c. The budget balance is the difference between tax revenue and government purchases.

So, budget balance= 0.2Y-450

d. Now if the consumer confidence decreases from 300 to 250, then the GDP as we calculated in part a will change to:

Y= 250+0.7(Y-0.2Y)+150+450+(40-0.15Y)

Y=890+.56Y-0.15Y

Y-.41Y=890

0.59Y=890

Y=890/0.59=1508.47