4- Unanticipated inflation

Question 1

What does the Phillips curve outline?

Answer 1

Negative relationship between inflation and unemployment rates

Question 2

What are the 5 defining features of the OLG island model?

Answer 2

-2 spatially separated islands
-Total population constant over time
-Old randomly split 50/50 across each island
-Young randomly split 1/3 2/3 on each island
-Population splits are independent across time

Question 3

How is money injected into the OLG island model?

Answer 3

Lump-sum subsidies are transferred to the old who are split equally across both islands

Question 4

What is the expression for the Money supply in a given period (Mₜ)?

Answer 4

Mₜ = zMₜ₋₁

Question 5

How many units of fiat money are printed in each period?

Answer 5

Mₜ - Mₜ₋₁ = (1-1/z)Mₜ

Question 6

What are the 2 main things young agents cannot observe?

Answer 6

-Number of young people on their island
-Size of subsidies to the old

Question 7

In what sense do agents have rational expectations in the OLG island model?

Answer 7

They know the possible outcomes they face and the probability of each one, so make the most correct inference possible on that basis

Question 8

What are the 3 main information limitations in the OLG island model?

Answer 8

-No communication between the islands
-Mₜ can be observed with a one period delay
-Rational expecations

Question 9

What are the young endowed with?

Answer 9

y units of time

Question 10

What 2 things can the young do with their endowment?

Answer 10

-Use it as leisure (c₁): non market good
-Use as labour (lₜ): market good, work to produce goods to sell to the old

Question 11

What is the quantity of goods from labour sold in the market (lₜ)?

Answer 11

Labour supply equals real money demand, when deciding how much to work effectively deciding how much money to demand
lₜᶦ = l(pₜᶦ) = vₜᶦmₜᶦ

Question 12

What is the budget constraint when young?

Answer 12

Units of leisure and labour cannot exceed units of time endowed
c₁ᶦ + lₜᶦ = c₁ᶦ + vₜᶦmₜᶦ = y

Question 13

What is the budget constraint when old?

Answer 13

Second period leisure cannot exceed value of goods sold when young and lump sum received when old
c₂ = vₜ₊₁mₜᶦ + aₜ₊₁

Question 14

Why does an increase in current prices (pₜ) induce the young to work more?

Answer 14

Price increases the rate of return to labour so the young are incentivised to work more, so more goods are produced

Question 15

What is the total demand for money on an island?

Answer 15

Labour supply of each young agent scaled to number of young agents
Nᶦl(pₜᶦ)

Question 16

What is the total supply of money on an island?

Answer 16

vₜᶦ(Mₜ/2)
Money supply/2 because half of the old are on each island

Question 17

Why is the price of goods high when the young population is small?

Answer 17

Each island has the same number of old, so when young are more scarce there is a higher relative demand for their goods, increasing prices and incentivising more production from each agent

Question 18

How do anticipated increases in money supply affect the OLG island model?

Answer 18

As z increases the rate of return on money falls, so money balances earnt by working are eroded by expanding money supply discouraging work to earn money thus leading to lower output

Question 19

How is money supply randomised for Unanticipated inflation?

Answer 19

Money supply is either kept constant with probability θ or doubled with probability 1-θ

Question 20

With Unanticipated inflation what are the 2 possible sources of a high price?

Answer 20

-Being on an island with a small number of young
-Increase in the money stock

Question 21

What happens if high price comes from a small number of young?

Answer 21

The young will want to sell a lot in the market because they anticipate a good average real return to their money balances

Question 22

What happens if high price comes from an increase in the money stock?

Answer 22

There is no reason to work hard because real return to labour won’t have increased

Question 23

What are the 4 possible states of the world in an OLG island model with unanticipated inflation?

Answer 23

-(zₜ = 1, young = 2/3N): pₜᵃ
-(zₜ = 1, young = 1/3N): pₜᵇ
-(zₜ = 2, young = 2/3N): pₜᶜ
-(zₜ = 2, young = 1/3N): pₜᵈ

Question 24

In which 2 states can agents be sure about the number of young?

Answer 24

-Constant money supply and abundant young yields the lowest price (pₜᵃ), so there must be many young
-Growing money supply and few young yields the highest price (pₜᵈ), so there must be fewer young

Question 25

In which 2 states are agents unsure about the number of young?

Answer 25

Middle cases of constant money supply and few young or vice versa yield the same price pₜᶜ = pₜᵇ so cause is ambigious

Question 26

What probabilities do the young assign to states b & c?

Answer 26

-State b: θ/2
-State c: (1-θ)/2

Question 27

What 2 things does the uncertainty about the true state of the island imply?

Answer 27

Each young supplies l, less than he would if he knew the population to be small and more than if he knew the population to be large
An intermediate price level, p, which is higher than pₜᵃ and lower than pₜᵈ

Question 28

Explain why the government cannot exploit the Phillips curve by inflating every period (Lucas critique)

Answer 28

Agents at the end of each period will observe there is a predictable pattern and adjust expectations (no longer random) disregarding states a & b because they will never occur