Quiz: Modeling Monetary Economies — 22 questions

1. What defines an overlapping generations economy?

A. Each period contains people from one age group

B. All individuals are born and retire in the same period

C. Young and old individuals coexist in the same period

D. Individuals remain young throughout their economic lives

Answer: (C)

Explanation

An overlapping generations economy has young and old individuals living simultaneously in each period. A single-generation economy instead lacks this coexistence of different age groups.

2. How long does a typical individual live in the overlapping generations model?

A. Three periods as young, middle-aged, and old

B. Two periods, first young and then old

C. Two periods, first old and then young

D. One period as young followed by retirement

Answer: (B)

Explanation

A typical individual lives through two periods: youth comes first, followed by old age. The initial old are a special case because they enter the model already old and live for one period.

3. If $N_t$ agents are born in period $t$, when do these agents become old?

A. In period $t-1$

B. During the same period $t$

C. After period $t+2$

D. In period $t+1$

Answer: (D)

Explanation

Agents born in period $t$ are young during that period and become old in period $t+1$. They do not become old at birth or remain young for an additional period.

4. How many young and old people are present in period $t$?

A. $N_{t-1}$ young and $N_t$ old

B. $N_t$ young and $N_{t-1}$ old

C. $N_t$ young and $N_{t+1}$ old

D. $N_{t+1}$ young and $N_{t-1}$ old

Answer: (B)

Explanation

The young population in period $t$ consists of those born in $t$, namely $N_t$, while the old population consists of those born in $t-1$, namely $N_{t-1}$. Reversing these indices confuses birth cohorts with current age groups.

5. What endowment does each individual receive over the two periods of life?

A. No goods when young and $y$ consumption goods when old

B. $y$ goods in each period of life

C. $y$ consumption goods when young and no goods when old

D. A fixed amount of goods that varies with age

Answer: (C)

Explanation

Each person receives $y$ consumption goods during youth and nothing during old age. The endowment is therefore concentrated in the first period of life rather than being evenly distributed.

6. What does nonstorability of the consumption good mean?

A. The good cannot be carried from one period into the next

B. The good can be transferred across periods without restriction

C. The good can be saved but loses part of its value

D. The good is produced and consumed within each individual’s lifetime

Answer: (A)

Explanation

Nonstorability means that goods from one period cannot be preserved for consumption in a later period. This rules out individual saving through physical storage, although it does not by itself describe intergenerational trade.

7. Why is trade between generations necessary in this economy?

A. People consume in one period, and goods remain available in the next

B. Young people receive no endowment, while old people receive all goods

C. Goods cannot be stored, while people desire consumption in both periods

D. The consumption good can be stored, but markets prevent individual saving

Answer: (C)

Explanation

Trade is necessary because the endowment arrives when people are young, goods cannot be stored, and individuals want consumption when old as well. The claim that young people receive no endowment reverses the model’s allocation.

8. What does the bundle $(c_{1,t},c_{2,t+1})$ represent for an individual?

A. Endowment when young and saving when old

B. Consumption when young and consumption when old

C. Consumption in two consecutive periods while young

D. Consumption when old and consumption when young

Answer: (B)

Explanation

The first component, $c_{1,t}$, is consumption when the individual is young, and the second component, $c_{2,t+1}$, is consumption when old. The subscripts identify life stage and calendar period rather than two types of endowment.

9. What does an indifference curve represent?

A. Bundles located at different utility levels along one curve

B. Points where consumption is equal across the two periods

C. Bundles that provide the same utility to an individual

D. Bundles that require the same endowment in each period

Answer: (C)

Explanation

An indifference curve connects consumption bundles that yield equal utility. Curves positioned toward higher utility represent different, higher utility levels rather than the same utility as the original curve.

10. For a differentiable utility function, how is the marginal rate of substitution calculated from an indifference curve?

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

B. $MRS = \frac{\partial U(c_1,c_2)}{\partial c_1}\times\frac{\partial U(c_1,c_2)}{\partial c_2}$

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

D. $MRS = \frac{\partial U(c_1,c_2)}{\partial c_1}+\frac{\partial U(c_1,c_2)}{\partial c_2}$

Answer: (C)

Explanation

The marginal rate of substitution is the absolute value of the indifference curve’s slope, given by the marginal utility of first-period consumption divided by the marginal utility of second-period consumption. Taking the reciprocal would reverse the direction of the trade-off.

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

A. The curve becomes flatter and the marginal rate of substitution decreases

B. The curve remains equally steep and the marginal rate of substitution is unchanged

C. The curve becomes steeper and the marginal rate of substitution increases

D. The curve becomes flatter while the marginal rate of substitution increases

Answer: (A)

Explanation

As $c_1$ increases along the indifference curve, the curve becomes flatter, so the absolute value of its slope and the marginal rate of substitution diminish. A steeper curve would instead indicate a larger marginal rate of substitution.

12. If an agent prefers bundle B to A and bundle C to B, what preference must transitivity imply?

A. The agent prefers C to A

B. The agent prefers A to C

C. The agent is indifferent between A and C

D. The agent forms a preference cycle among the bundles

Answer: (A)

Explanation

Transitivity carries the preference from B over A and C over B to a preference for C over A. A preference cycle would instead represent intransitivity, not transitivity.

13. What does transitivity imply about two indifference curves in a standard preference relation?

A. They must have identical slopes

B. They must be parallel

C. They cannot cross

D. They must intersect once

Answer: (C)

Explanation

If indifference curves crossed, the same bundles could generate conflicting preference rankings, violating transitivity. Parallelism and identical slopes are not required by transitivity.

14. How do the initial old behave in the overlapping-generations model?

A. They consume in the initial period and maximize consumption subject to their endowments

B. They receive the same allocation as every later generation

C. They work in every period and save for the next generation

D. They trade with future generations to maximize lifetime utility

Answer: (A)

Explanation

The initial old live and consume only during the initial period, choosing consumption subject to their available endowments. They do not have a future working or saving period within the model.

15. Which institutional arrangement distinguishes centralized from decentralized solutions?

A. Households allocate resources centrally, while firms determine the decentralized money supply

B. A government sets prices centrally, while households eliminate trade in the decentralized outcome

C. A benevolent planner allocates resources centrally, while monetary trade coordinates the decentralized outcome

D. Monetary trade allocates resources centrally, while a planner coordinates the decentralized outcome

Answer: (C)

Explanation

The centralized solution is implemented by a benevolent planner, whereas the decentralized solution operates through trade using money. The alternative arrangements reverse or misstate these coordinating mechanisms.

16. If each young person produces y units in period t and there are N_t young people, what resources are available to the planner in that period?

A. $N_{t-1} c_{2,t}$

B. $N_t c_{1,t}$

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

D. $N_t y$

Answer: (D)

Explanation

The planner’s available resources equal the number of young people multiplied by each young person’s output, giving $N_t y$. Young consumption is an allocation of those resources rather than the resource total itself.

17. Under equity, how are total young and old consumption represented in period t?

A. Young consumption is $N_t y$ and old consumption is $N_{t-1} c_{1,t}$

B. Young consumption is $N_t c_{1,t}$ and old consumption is $N_{t-1}c_{2,t}$

C. Young consumption is $N_t c_{2,t}$ and old consumption is $N_{t-1}c_{1,t}$

D. Young consumption is $N_{t-1} c_{1,t}$ and old consumption is $N_t c_{2,t}$

Answer: (B)

Explanation

Equity gives every member of generation t the same young allocation, so total young consumption is $N_t c_{1,t}$; the preceding generation’s old consumption is $N_{t-1}c_{2,t}$. The other expressions mismatch generations or consumption stages.

18. Which inequality describes feasible total consumption in period t?

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

B. $N_t c_{1,t}+N_{t-1}c_{2,t}=N_{t-1}y$

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

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

Answer: (A)

Explanation

Feasibility requires aggregate consumption by the young and old to be no greater than aggregate output, yielding the stated inequality. Reversing the inequality or switching population indices does not represent the planner’s resource constraint.

19. Which condition characterizes a stationary allocation?

A. Each generation receives a different consumption pattern as population changes

B. Only the initial generation receives a fixed consumption pattern

C. Every generation receives the same lifetime consumption pattern across dates

D. Consumption is fixed within a period but changes across generations

Answer: (C)

Explanation

A stationary allocation is unchanged across generations: young consumption is represented by $c_1$ and later-life consumption by $c_2$ at every date. An allocation that varies across generations is nonstationary.

20. For a stationary allocation with a constant population, what feasibility condition must hold?

A. $c_1+c_2\leq y$

B. $c_1-c_2\leq y$

C. $c_1c_2\leq y$

D. $c_1+c_2\geq y$

Answer: (A)

Explanation

With a constant population, the planner’s aggregate constraint reduces to $c_1+c_2\leq y$. A sum above output violates feasibility, while subtraction and multiplication do not express the resource constraint.

21. What is the golden rule allocation in an overlapping-generations economy?

A. The stationary feasible allocation that maximizes future generations’ welfare measured by $U(c_1,c_2)$

B. The feasible allocation that maximizes consumption for the initial old

C. The nonstationary allocation that gives each generation a different lifetime utility

D. The stationary allocation that maximizes current output without considering consumption

Answer: (A)

Explanation

The golden rule selects a stationary allocation within the feasibility set that maximizes the welfare of future generations, represented by $U(c_1,c_2)$. Maximizing the initial old’s consumption defines a different objective.

22. What objective defines the initial-old optimal allocation?

A. Maximizing utility for all future generations subject to stationarity

B. Maximizing total output regardless of the resulting allocation

C. Maximizing consumption for the initial old subject to feasibility

D. Equalizing consumption between the young and the old in every period

Answer: (C)

Explanation

The initial-old optimal allocation is the feasible allocation chosen to maximize consumption for those who are old in the initial period. The golden rule instead evaluates welfare for future generations, so the two objectives need not coincide.