Overlapping generations model

Question 1

Model skeleton

Answer 1

• Individuals live for two periods:
  
  • youth
  • old age
• Number of individuals born at time t is N_t, there is an exponential population growth
• Young age
  
  • ​They work and decide how much to consume and and save.
• Old age:
  
  • ​They don’t work, so they just consume their savings.

Question 2

Household problem

Answer 2

Question 3

Savings and labor income

Answer 3

If individuals don’t work in second period

Labor income only generates income effect => increases consumption in both periods.

• It also increases savings

Question 4

Savings and interest rate

Answer 4

• Generates two opposing forces:
  
  • Substitution effect => cost of consumption today increases => I save more
  • Income effect => increases intertemporal income (if I save) => consume more in both periods.

Question 5

Firm problem

Answer 5

Usual structure, there are no capital gains

Question 6

Equilibrium

Answer 6

Question 7

Law of motion of capital per capita

Answer 7

Question 8

Properties of the steady state

Answer 8

Question 9

Properties of the steady steady state (non-oscilatory trajectories)

Answer 9

Then income effect shouldn’t be too strong

Question 10

Overlapping generations and pareto optima

Answer 10

• In the overlapping generations oversaving (dynamic inefficiency is possible)
• There is scope for a Pareto improving government intervention
• This happens because there is a market missing (intergenerational transfers)
  
  • Whenever r<n></n>
  </n>

Question 11

Problem under altruism

Answer 11

Individuals care about themselves and the utility of their children

Question 12

Altruism and dynamic efficiency

Answer 12

• Non negativity of the bequests isn’t binding
• With altruism there is no over accumulation: decentralized solution is Pareto efficient.

Question 13

Fully funded system

Answer 13

• There is no effect over the consumption levels.
• Notice now the market clearing condition includes the Government saving
• Both forms of savings yieldthe same return and the household is indifferent between them
• Fully funded system can change the consumption allocations if households can’t borrow against future pensions and the government sets very high contributions

Question 14

PSYG system

Answer 14

• Imposed steady state condition is equal contributions per person accross periods:

d1t=d1,t+1

• Here, there is no savings from the government, it is just a transfer from the young to the old intra-period

Question 15

Savings and PAYG

Answer 15

• PAYG system has a lower level of capital per capita in the SS

Question 16

Transition from a PAYG to a fully funded

Answer 16

• Government issues debt that is refinanced perpetually
• Government now competes for private savings
• If we are at the golden rule, there is no change in the final allocations from the pension system reform