# ECO209Y5 Lecture Notes - Lecture 7: Ricardian Equivalence, Government Spending, Competitive Equilibrium

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Natalie Ianniello

ECO209

Tewk

October 26, 2015

Lecture #7 – Consumption-Savings Decisions Part II

Government spending is exogenous

Period one constraint - G = T + B

- B = bonds (borrowing)

T = total taxes

T = Nt

- t = tax per individual

- N = number of consumers

Government can borrow in the two period model

They can borrow money and spend more than Nt in this model

Period two constraint – G1 + (1+r)B = T1

In period two it must repay what it borrowed

PLEASE NOTE THE DIFFERENT IN BIG T AND LITTLE t DURING THIS LECTURE

Governments Lifetime Budget Constraint:

B = (T1-G1)/1+r

Competitive Equilibrium:

Consumer choices must be optimal

CE is set of:

- Endogenous consumption quantities (c, c1, s)

- Endogenous aggregate quantities (C, C1, T, T1)

- Equilibrium interest rate – r

Given:

- (t, T1, r) of each N consumers are optimal

- Governments lifetime BC holds

- Credit market clears (aggregate private savings = government debt)

Ricardian Equivalence Theorem:

Theory – consider a given amount of government spending (G, G1). Suppose

government wishes to change current taxes T. Then as long as lifetime BC is

satised, there is no change in interest rate or consumption bundles

Consumers know tax cut today means higher taxes tomorrow

Fall in change in T, B will increase by the change in T

Next period, the government needs to repay an additional (1+r) change in T

Therefore, T1 will rise by (1+r) change in T to repay it

Dividing all of this by N will give you how much each consumer pays in taxes