Week 8: Consumption and Savings Flashcards
Consumption and Savings Model - periods, income, taxes, consumers
2 periods - current and future
income - exogenous
lump sum taxes
consumers can be different
Current Period Equation
y-t = c+s
When is someone a lender?
savings > 0
When is someone a borrower?
savings < 0
Bond
A promise to pay in the future with 1 + r consumption good in exchange for 1 unit of consumption of the good today
Future period equation
c’ = y’ - t’ + (1+r)s
Lifetime Wealth
quantity of resources available to consumer in current consumption goods to spend on consumption goods over lifetime (2 periods)
Intertemporal Budget Constraint Definition
constraint faced by a decision maker who is making choices for both the present and future
Intertemporal Budget Constraint Equation
c + c’/(1+r) = y- t + (y’-t’/1+r)
C(1) + C(2)/(1+r) = Y(1) + Y(2)/(1+r)
Lifetime Wealth Equation
a = y + y’/(1+r) - t - t’/(1+r)
Lender and Borrower Diagram - Points X,Y,E
All labels
Optimal Choice of Lender Diagram
Optimal Choice of Borrower Diagram
Marginal Rate of Substitution (MRS)
the amount of a good that a consumer is willing to consume compared to another good, as long as the good is equally as satisfying
What happens as a result of an increase in current and future disposable income? (3 things)
- current and future consumption increases
- saving increases
- consumer acts to smooth consumption over time
Increase in current disposable income diagram
Increase in current disposable income equation
Increase in future disposable income diagram
Increase in Real Interest Rate for Lender Diagram
What happens to future consumption, current consumption and saving when interest rate rises for a lender?
c’ increases
c may increase or decrease
s may increase or decrease
What happens to future consumption, current consumption and saving when interest rate rises for a borrower?
c’ may increase or decrease
c decreases
s increases
Increase in real interest rate for borrower diagram
Government Tax Revenue Equations in Each Period
First period = T =N(t)
Second period = T’ = N(t’)
N = constant population
Government Budget Constraint First Period
G = T + B T = taxes B = debt
Government Budget Constraint Second Period
G’ + (1+r)B = T’
Government Intertemporal Budget Constraint
G + G’/(1+r) = T + T’/(1+r)
What 3 things happen in competitive equilibrium?
- Consumers optimally choose current and future consumption given interest rates
- gov intertemporal budget constraint is satisfied
- credit market clears
Credit Market Equilibrium Diagram
Ricardian Equivalence Definition
economic theory that suggests that increasing government deficit spending will fail to stimulate demand as it is intended
Endowment Point Definition
The initial allocation of the market
Optimal Choice and Ricardian Equivalence Diagram
Diagram:
Credit Market Equilibrium and Ricardian Equivalence
When is Ricardian Equivalence not satisfied? (4 times)
- Tax changes are different for different consumers
- If someone dies in the first period
- if taxes are not lump sum
- If the credit market is not perfect , different interest rates for lenders and borrowers
How to calculate the intertemporal budget constraint
- should have 2 budget constraints in the form consumption = incomes - savings
- combine the two and get intertemporal budget constraint
PV of Consumption Equation
PV of consumption = financial wealth + human wealth
What is the PV of labour income?
Human wealth
Utility Definition
Total satisfaction received from consuming a good or service
What does utility depend on?
Consumption today and in the future
Utility Equation
Diminishing Marginal Utility
the decrease in satisfaction a consumer has from consuming an extra unit of a good or service
What does it mean if β < 1 in utility equation?
- future consumption is discounted
- todays consumption is valued more than future consumption
What does it mean if β = 1 in utility equation?
current and future consumption is treated equally
How do you maximise utility subject to budget constraint?
When is utility maximised?
When agents are indifferent between consuming more today or more tomorrow
What choices do agents have when maximising utility?
Either:
- consume today
- consume 1+r units in the future
Euler Equation
What does the Euler equation show?
Marginal utility of consuming 1 more unit today = discounted marginal utility of consuming 1+r units in the future
Marginal Utility
The added satisfaction a consumer gets from consuming one more unit of a good or service
Method to Solve Euler Equation
- u(c) = log(c)
- derive u’(c) = 1/c
- Equation becomes 1/c(t) = β(1+r) 1/c(t+1)
- rearrange equation becomes c(t+1)/c(t) = β(1+r)
What does the Euler equation explain?
explains how interest rates and growth rates are related
What does a lower β in euler equation show?
impatient, consumption growth is lower
What does a higher β in euler equation show?
patient, consumption growth is faster
What do you need to solve for optimal consumption today and in the future?
Euler equation and intertemporal budget constraint
Method to solve consumption for today and in the future if β = 1
