overlapping generations (OLG) model : equillibrium and first welfare theorem Flashcards
why did paul sameulson invent the OLG model?
aul Samuelson invented
the OLG model to study economic interactions among people at different stages of their life cycles
what is the framework of the simple overlapping generation model?
no production takes place in the
samuelson model
in each time period there is one commodity, a generic perishable consumption good
assume one person in each generation and each young person survives to old age with 100% certainty
there is only two generations - when the next time period arrives the previous old generation have all died and the young generation are now old
what is the utility maximisation choice for generation 0?
c^o_1 = w^o_1 where w_1 is endowment of genereric good in period 1 and c_1 is consumption of generic good. as generation 0 lives for one time period and there is one consumption good they are equal
what is the budget constraint for young when generation t>=1 is young at t, old at t+1 and dead at t+2?
c^y_t +s_t <= w^y_t where c^y_t is consumption of youth at period t , s_t is saving of youth and w^y_t is endowment of generic good for a young person in period t
what is the budget constraint for old when generation t>=1 is young at t, old at t+1 and dead at t+2?
c^o_t+1 <= (1+r_(t+1))s_t +w^o_t+1 where c^o_t+1 is consumption of old in period in period t+1, principal plus interest of (1 + r_t+1)s_t at maturity the next period
what is the lifetime budget constraint for generation t>=1?
what is the solution to the cobb douglas utility function maximisation of the standard OLG model for lifetime consumption?
what is the solution for the savings rate for the standard OLG model for lifetime consumption?
what is the national income identidy and how does this change for the standard OLG model ?
how is the national income identidy used for the OLG Model for individuals?
how is the market clearing interest rate derived?
how can the market clearing interest rate be used to calculate the consumption levels and savings rate?
how do you determine that the savings is equal to zero and consumption is equal to initial endowment?
is it possible to get a pareto superior allocation?
Suppose there is heterogeneity within generations: among the consumers born in period t ≥ 1, not all
have the same utility function and/or not all have the same endowment vector. Can we still conclude
that no trade takes place in the competitive equilibrium? Explain. A descriptive explanation (without
equations) is sufficient.?
