1. Consumer Choice With Uncertainty Part I: Intertemporal Choice
Agenda:
Uncertainty & The Universe
Sources of Uncertainty Brainstorm
Key math: Present and Future Value
Intertemporal Choice
Economic Modeling & Policy Implications

2. “The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature…By showing the world how to understand risk, measure it, and weight its consequences, they converted risk-taking into one of the prime catalysts that drives modern Western Society.”

3. Demand Over Time (“Intertemporal Choice”)
Later
Now!
A very small extension…

4. The Intertemporal Budget Constraint
tomorrow
Optimal Bundle: Marginal rate of intertemporal substitution=slope of budget
Endowment Bundle:
What you get today and tomorrow
Question: How can we spend more today than our income?
today
How can we spend more than our income today?
“Present value of lifetime income”

5. Key math concept: Present Value
A dollar today is not worth the same as a dollar tomorrow.
The present value is the value divided by 1+ the risk-free interest rate.
Example:
Congratulations! You won $1,000 in the lottery, BUT, you can’t collect it for a year. If the risk-free rate is 10%, how much is your lottery ticket worth today?
Look for comic re: present value
Need to color and animate

6. Time Value with Multiple Time Periods
The Mi and ri can change each time period!
Example:
Congratulations! You won $1,000 in the lottery. You will be paid $500 today, $300 next year and $200 in two years. The interest rate for one year is 5% and the interest rate for two years is 7%. What is the present value of your winnings?

7. Key math concept: Future Value
The future value is the present value multiplied by 1+ the risk-free interest rate raised to the power of the number of time periods (compound interest).
Example:
Congratulations! You won $1,000 in the lottery. If you collect the money today and put it in the bank at 10% annual interest, how much will it be worth in one year?
Note that compound interest is more than simple interest (500)
How much will it be worth in five years?
Read about delayed gratification and success:

8. Another Future Value problem…
Congratulations! You won $1,000 in the lottery. If you receive $100 per year for 10 years and save all of your earnings at an interest rate of 10% what is the future value of your winnings in year 10 (right after you get your last payment)?
How much of your earnings would you give up (e.g. how much less than $1,000) would you accept to get the lump sum today?

9. Save to spend more tomorrow
Congratulations! You just got a new job that pays you $500 per week. The interest rate is 3%. Draw a graph & answer the following:
1. What is the present value of your income for two weeks?
2. What is the future value of income for two weeks?
3. What is your endowment bundle?
4. If your marginal rate of intertemporal substitution at your endowment bundle is 1, should you a) live pay check to pay check; b) borrow to spend more today or c) save to spend more tomorrow?
$1,015
Endowment Bundle
($500, $500)
MRIS = 1
Optimal Bundle
MRIS = 1.03
Save to spend more tomorrow
What if the interest rate rises to 5%?
What if the interest rate drops to 0.5%
$985.44

10. Interest Rates and the Intertemporal Budget Constraint
What happens if interest rates go up?
The intertemporal budget constraint PIVOTS around the original endowment.
BOTH the X and Y intercepts change!
When interest rates go UP we have more money tomorrow if we save, and less today if we discount future earnings.
What happens if interest rates go down?
(M1, M2 ) is the endowment bundle
When interest rates go DOWN we have less money tomorrow if we save, but tomorrow’s dollars are worth more today.
It depends on your time preference and the shape of our indifference curve!
Will you be happier if interest rates go UP or DOWN?

11. Beta – a time consistent discount rate
Looking ahead…
What if we have inconsistent time preferences?

12. Static and Dynamic Economic Models
Type of Optimization Notational Set-up
Form of Answer
Static optimization
One period
A number
Multi-period
Series of discrete time problems
A vector of numbers
Dynamic Optimization
Calculus of Variations
Euler Equation
Optimal path
Not just the change in value,
but the change in the curve
Optimal control
Maximum Principal
Optimal paths (curves) for
state, control & co-state
Dynamic Programming
Principal of
Optimality
Decision Rule
optimal control path

13. Policy issue: dynamic scoring

14. the higher the discount rate
Policy Summary
The higher the risk,
the higher the discount rate
Times of war
Risky new businesses
Individuals with terminal illness – less uncertainty, lower discount!
Monetary Policy
Lower rates get people to spend more now!
Lower rates mean lower hurdles for project investment
Higher rates take money out of the economy now, increasing hurdle rate for projects, reducing threat of inflation