Overlapping Generations (OLG)

Eco 302Nov 16, 2012

First Welfare Theorem

• Market outcomes are Pareto efficient– We can’t make anyone better off without making

someone else worse off.• If we expand the Solow model to allow people to

choose labor and savings (RCK), they reach the Golden Rule level of savings.

• Wrong stuff about the 1st Theorem corrected

Hiding in the Background

• Decreasing returns to consumption

Hiding in the Background• Suppose you sometimes have low consumption

and sometimes high. • What is your average utility? – Green line.

Hiding in the Background• Suppose you always have the average consumption.• What is your average utility? – Blue line.

So, do you want blue or green?

A fable

• Island with two types of people: old and young• Young people can work hard: 3 food• Old people: 1 food

• Problem 1: Can’t save the food• Problem 2: Can’t trade. We only meet once.

Solution 1

• Really nice people – Social capital• Rule: You take care of Grandpa

• Option 2: People are altruistic

Solution 2: Government Social Security

• Gov taxes the young: 1 food• Gov gives the old: 1 food

• Old obviously better off• Young better off in the long run• Population growth is good

• Pay-as-you-go PAYG Social Security

Why does this work?

• Imagine there were a last generation and then the world ends.

• Take 1 from the young. Give 1 to the old• Next generation, the young are dead. They are

made worse off.

• Government improves on the market allocation.

US case

• 1930s Great Depression – savings wiped out• Very few old (don’t live long) and lots of Young• Started completely as PAYG

• We can read the writing on the wall – OLD/Young is getting bigger

Can we do it without government?

• Chocolate arrives in a gold foil• We can’t do anything with the gold foil• UNTIL

The Talk

• OLD: I would like to buy your food for this gold foil.• YOUNG: Why would I do that?• OLD: Because someday you will be OLD. And you will go to your son,

as I am going to you, and you will offer to buy food from your son with this gold foil.

• YOUNG: Why would he sell me food?• OLD: Because you will tell him the same thing• …• YOUNG: Okay

Why does this work?

• Imagine there were a last generation and then the world ends. Call that time T.

• In time T – The Young will not take the money.• In time T-1 – The Young will not take the money.• In time T-2 – The Young will not take the money.• In time T-3 – The Young will not take • …• In today – The Young will not take the money• Backward Induction

The End of the World

• 1996 Baptists. ~6-12 months before the End of the World: quit job, sold house– Partied– Traveled to Holy Land– The world didn’t end.

• 2000 Y2K• 2012

• Experimental Economics

Why do we have money?

• Acceptable – an agreed on illusion• Generates trade that would NEVER happen • Money = power, class struggle (Marxist)• Free market works again without government,

without CBN (Libertarian)

What can you do?

• See the link between money supply and price level– More M, more P– There is NO upward sloping supply curve

• Suppose M grows faster than N.– If m>n, Price level reaches infinity– If m<n, Price level reaches 0– The only sustainable outcome: m=n

What have we done?

• Where money comes from• Social Security• Trade where we can’t save• Population dynamics impact the economy• Rule for CBN: let m be a constant (preferably n)• The End of World– Life keeps going on as long as most of you don’t believe

the world will end– Self-fulfilling prophecy: IF we all believe it