2- Benchmark OLG model Flashcards
What is the basic Economic problem for agents in the OLG model?
Each future generation has access to nonstorable good only when young but wants to consume in both periods to maximise lifetime utility
What is the centralised/social planner solution?
Optimal allocation in the economy subject only to the resource constraint
What is the decentralised solution?
Allocation of goods with agents trading amongst each other
How do we know if the decentralised solution is optimal?
If centralised and decentralised solutions are identical then market can achieve optimal allocation
Why does equality of market and social planner solution imply optimality?
The social planner looks at all goods in the economy and maximises utility pareto efficiently such that no agent can be made better off without another being worse off
What is the social planner’s resource constraint?
Total amount of consumption good available:
Nₜy = Nₜc₁ₜ + Nₜ₋₁c₂ₜ₊₁
How is there equity in allocation to each generation?
Every member of a generation gets the same allocation but there may be a difference between old and young
How does assuming constant population and stationary equilibrium change resource constraint?
Nₜ=Nₜ₋₁=N and time subscripts can be removed such that: y ≥ c₁ + c₂
Why does the resource constraint hold at equality?
Since the consumption good is perishable, it is inefficient to leave any undistributed at all
How can you find optimal consumption c₁* & c₂* from a utility function?
Rearrange the resource constraint to get each variable in terms of the other, sub into utility function and differentiate for each FOC
What is the Golden rule (optimal) allocation?
Feasible, social planner allocation that maximises the welfare of future generations
Why is there a lack of double coincidence of wants between generations?
Young are endowed with consumption good but the old are not i.e. the young have what the old want but the old have nothing the young want
How can trade with credit work?
If there is perfect record keeping and full commitment, young people will transfer some of their endowment to the old so that others will do the same for them in the next period
How does trade with credit breakdown?
If record keeping is imperfect and young people can fake transfers to the old then the incentive mechanism breaks down
What are the 3 defining characteristics of a competitive monetary equilibrium?
-Mutually beneficial trades: utility maximisation
-Agents are price takers (actions don’t move price)
-Markets clear (supply=demand)
In OLG model, how do central banks roll out money to the economy?
Central bank equally distributes M units of fiat money to the initial old such that they each have m=M/N
What does the implementation of money mean for the OLG model?
Young willing to sell goods to old for money. Uses money when old to buy good from young allowing agents to consume in both periods. Overcomes the lack of double coincidence of wants
What is the value of money (vₜ)?
The number of goods one must give up to obtain 1 dollar- the inverse of the price level:
vₜ = 1/pₜ
What is the real rate of return of fiat money?
How many goods can be bought in period t+1 if 1 unit is sold for money in period t:
vₜ₊₁/vₜ = pₜ/pₜ₊₁
What is the real demand for fiat money (q)?
The number of goods an agent chooses to sell for fiat money i.e. goods not consumed when young:
q = y - c₁
What is the difference between c₁ & c₂?
-c₂ is a market good: it has been traded from young to old
-c₁ is a non market good: portion of own endowment that young consume
What is an agent’s first period budget constraint?
Goods consumed in first period and value of goods sold for money cannot exceed endowment:
y = c₁ + vₜmₜ
What is an agent’s second period budget constraint?
Second period consumption cannot exceed value of money generated from selling goods in first period:
vₜ₊₁mₜ = c₂
What is an agent’s lifetime budget constraint?
First period consumption and discounted second period consumption cannot exceed endowment:
y ≥ c₁ + (vₜ/vₜ₊₁)c₂
