2- Benchmark OLG model

Question 1

What is the basic Economic problem for agents in the OLG model?

Answer 1

Each future generation has access to nonstorable good only when young but wants to consume in both periods to maximise lifetime utility

Question 2

What is the centralised/social planner solution?

Answer 2

Optimal allocation in the economy subject only to the resource constraint

Question 3

What is the decentralised solution?

Answer 3

Allocation of goods with agents trading amongst each other

Question 4

How do we know if the decentralised solution is optimal?

Answer 4

If centralised and decentralised solutions are identical then market can achieve optimal allocation

Question 5

Why does equality of market and social planner solution imply optimality?

Answer 5

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

Question 6

What is the social planner’s resource constraint?

Answer 6

Total amount of consumption good available:
Nₜy = Nₜc₁ₜ + Nₜ₋₁c₂ₜ₊₁

Question 7

How is there equity in allocation to each generation?

Answer 7

Every member of a generation gets the same allocation but there may be a difference between old and young

Question 8

How does assuming constant population and stationary equilibrium change resource constraint?

Answer 8

Nₜ=Nₜ₋₁=N and time subscripts can be removed such that: y ≥ c₁ + c₂

Question 9

Why does the resource constraint hold at equality?

Answer 9

Since the consumption good is perishable, it is inefficient to leave any undistributed at all

Question 10

How can you find optimal consumption c₁* & c₂* from a utility function?

Answer 10

Rearrange the resource constraint to get each variable in terms of the other, sub into utility function and differentiate for each FOC

Question 11

What is the Golden rule (optimal) allocation?

Answer 11

Feasible, social planner allocation that maximises the welfare of future generations

Question 12

Why is there a lack of double coincidence of wants between generations?

Answer 12

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

Question 13

How can trade with credit work?

Answer 13

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

Question 14

How does trade with credit breakdown?

Answer 14

If record keeping is imperfect and young people can fake transfers to the old then the incentive mechanism breaks down

Question 15

What are the 3 defining characteristics of a competitive monetary equilibrium?

Answer 15

-Mutually beneficial trades: utility maximisation
-Agents are price takers (actions don’t move price)
-Markets clear (supply=demand)

Question 16

In OLG model, how do central banks roll out money to the economy?

Answer 16

Central bank equally distributes M units of fiat money to the initial old such that they each have m=M/N

Question 17

What does the implementation of money mean for the OLG model?

Answer 17

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

Question 18

What is the value of money (vₜ)?

Answer 18

The number of goods one must give up to obtain 1 dollar- the inverse of the price level:
vₜ = 1/pₜ

Question 19

What is the real rate of return of fiat money?

Answer 19

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

Question 20

What is the real demand for fiat money (q)?

Answer 20

The number of goods an agent chooses to sell for fiat money i.e. goods not consumed when young:
q = y - c₁

Question 21

What is the difference between c₁ & c₂?

Answer 21

-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

Question 22

What is an agent’s first period budget constraint?

Answer 22

Goods consumed in first period and value of goods sold for money cannot exceed endowment:
y = c₁ + vₜmₜ

Question 23

What is an agent’s second period budget constraint?

Answer 23

Second period consumption cannot exceed value of money generated from selling goods in first period:
vₜ₊₁mₜ = c₂

Question 24

What is an agent’s lifetime budget constraint?

Answer 24

First period consumption and discounted second period consumption cannot exceed endowment:
y ≥ c₁ + (vₜ/vₜ₊₁)c₂

Question 25

What is the aggregate real demand for money (Mᵈ)?

Answer 25

Real demand for money scaled up to whole population:
Mᵈ = Nₜq = Nₜ(y-c₁)

Question 26

How can you express the aggregate real supply of money (Mˢ) decided by the central bank?

Answer 26

Money distributed scaled to its real value
Mˢ = vₜMₜ

Question 27

Describe a money market equilibrium

Answer 27

Money supply = money demand:
vₜMₜ = Nₜ(y-c₁)

Question 28

How do you find the real rate of return for fiat money (vₜ₊₁/vₜ)?

Answer 28

-Solve the money market equilibrium for vₜ
-Add +1 to t subscripts for vₜ₊₁
-Put vₜ₊₁ over vₜ

Question 29

How can you express the real demand for money (q) in terms of real money value?

Answer 29

q = vₜmₜ

Question 30

When is the demand for money utility maximising?

Answer 30

When the marginal rate of substitution between first and second period consumption equals the rate of return of money

Question 31

How can you evaluate whether markets can achieve optimal allocation without a utility function?

Answer 31

Compare resource constraint and lifetime budget constraint

Question 32

Briefly outline how a growing population changes the OLG model?

Answer 32

Each agent is still endowed with y units when young but total number of goods available when old is
higher: Nₜy > Nₜ₋₁y

Question 33

What is the social planner’s resource constraint when the population grows at rate n?

Answer 33

c₁ + (1/n)c₂ = y

Question 34

How does a growing population affect the real growth rate of money?

Answer 34

Given constant money supply, the real value of money increases with population because the same money bids for more goods

Question 35

What does a positive real growth rate of money mean?

Answer 35

The value of fiat money increases over time so the price of consumption goods decreases over time

Question 36

What is the formula for growth rate of the money supply (z)?

Answer 36

Mₜ₊₁/Mₜ