Flashcards: Modeling Monetary Economies — 33 cards

What defines an overlapping generations economy?

Young and old individuals coexist in the same period.

How long do individuals live in the overlapping generations model?

Individuals live for two periods, young then old.

What happens to agents born in period t in the overlapping generations model?

They become young in period t and old in period t+1.

How long do initial old individuals live at t = 1?

They live for only one period.

How many young people are in the economy each period?

There are $N_t$ young people each period.

How many old people are in the economy each period?

There are $N_{t-1}$ old people each period.

What is an endowment in this economy?

An endowment is the consumption goods an individual receives when young.

How many consumption goods does an individual receive when old?

Individuals receive nothing when old.

What is the storage rule for the single consumption good?

The single consumption good cannot be stored from one period to the next.

Why is trade between generations necessary?

Because goods cannot be stored and individuals want consumption in both periods.

What does a consumption bundle specify in intertemporal preferences?

An individual's consumption when young and when old.

What does an indifference curve connect in consumption bundles?

Bundles that yield the same utility to an individual.

What is the formula for the marginal rate of substitution (MRS)?

$MRS = \frac{\partial U(c_1,c_2)/\partial c_1}{\partial U(c_1,c_2)/\partial c_2}$

What does the marginal rate of substitution represent on an indifference curve?

The absolute value of the curve's slope.

How does the indifference curve slope change as $c_1$ increases?

The curve becomes flatter.

What happens to the marginal rate of substitution as $c_1$ increases along the indifference curve?

It diminishes.

What does transitivity require if an agent prefers B to A and C to B?

The agent must prefer C to A.

What does transitivity require if bundles B and A are equally preferred and C and B are equally preferred?

Bundles A and C must be equally preferred.

What does transitivity imply about indifference curves?

Indifference curves cannot cross.

When do the initial old live and consume?

Only in the initial period.

How do the initial old maximize consumption?

Subject to their endowments.

What distinguishes the centralized from the decentralized solution?

The centralized solution uses a benevolent planner, the decentralized uses trade with money.

What formula gives the planner's available resources in period t?

The planner's resources equal $N_t y$.

Under equity, how is total young consumption in generation t expressed?

Total young consumption is $N_t c_{1,t}$.

Under equity, how is total old consumption in period t expressed?

Total old consumption is $N_{t-1} c_{2,t}$.

What is the feasibility condition for total consumption in period t?

$N_t c_{1,t} + N_{t-1} c_{2,t} \leq N_t y$.

With constant population, what equality holds between $N_t$ and $N_{t-1}$?

$N_t = N_{t-1} = N$.

What is the feasibility condition for consumption with constant population?

$c_{1,t} + c_{2,t} \leq y$.

What does a stationary allocation give every generation?

The same lifetime consumption.

What is the feasibility condition for a stationary allocation with constant population?

$c_1+c_2\leq y$

What does the golden rule allocation maximize?

The welfare of future generations measured by U(c1,c2).

What does the initial-old optimal allocation maximize?

Consumption for the initial old.

Why can the golden rule allocation and initial-old optimal allocation differ?

Because they maximize welfare for different groups.