Question 1

If there are consumption externalities, then a competitive equilibrium is not necessarily Pareto optimal.

Accepted Answer

Consumption externalities occur when a person's consumption affects the utility or welfare of others. In such cases, the competitive market equilibrium may not lead to a Pareto optimal outcome as it does not take into account the external effects on other individuals. Therefore, interventions like taxes or subsidies may be necessary to align private and social incentives and achieve a Pareto efficient outcome.

Question 2

A pure exchange economy is an economy where goods are traded but there is no production.

Accepted Answer

In a pure exchange economy, individuals only trade goods and services that they own, but there is no production of goods within the economy.

Question 3

Jack Spratt's utility function is U(F, L) = L. His wife's utility function is U(F, L) = F. If Jack's initial endowment is 40 units of F and 20 units of L and if Jack's wife's initial endowment is 24 units of F and 40 units of L, then in an Edgeworth box for Jack and his wife, an allocation of F and L will be Pareto optimal only if it is at a corner of the box.

Accepted Answer

False

Question 4

In a competitive pure exchange economy, if the total value of excess demand for all types of food is zero, then the total value of excess demand for all nonfood commodities must be zero.

Accepted Answer

This statement is known as the Walras' Law, which states that in a competitive pure exchange economy, if the total value of excess demand for all but one of the commodities is zero, then the excess demand for the last commodity must also be zero. Therefore, if the excess demand for all types of food is zero, the excess demand for all nonfood commodities must also be zero.

Question 5

If two people have identical homothetic preferences and if their indifference curves have a diminishing marginal rate of substitution, then in an Edgeworth box, the locus of Pareto optimal allocations between them is a diagonal straight line.

Accepted Answer

This is because when two people have identical homothetic preferences, their indifference curves are parallel straight lines that emanate from the origin. This implies that their MRS is constant and diminishing along each of their indifference curves. In an Edgeworth box, the Pareto optimal allocations occur along the contract curve, which is the locus of points where the MRS of one person equals the MRS of the other person for every commodity. Since their MRSs are identical and diminish at the same rate, the contract curve is a diagonal straight line.

Question 6

In a model with two consumers, two goods, and no production, the contract curve must be a line going from one consumer's origin to the other consumer's origin.

Accepted Answer

The answer of In a model with two consumers, two...

Question 7

Partial equilibrium analysis concerns only supply or only demand while general equilibrium analysis deals with supply and demand at the same time.

Accepted Answer

Partial equilibrium analysis focuses on either supply or demand while general equilibrium analysis considers both supply and demand simultaneously.

Question 8

From Walras's law it follows that in a market with two goods, if demand equals supply in one market, then demand must equal supply in the other market.

Accepted Answer

Walras's law states that if there are n-1 markets in equilibrium, then the nth market must also be in equilibrium. In a market with two goods, if demand equals supply for one of the goods, then it implies that the excess supply or demand must be accounted for by the second good, leading to an equilibrium in the second market as well. Therefore, demand must equal supply in both markets.

Question 9

If allocation x is a competitive equilibrium at prices p and if everybody likes his bundle in allocation y better than his bundle in allocation x, then the total value of allocation y at prices p exceeds the total value of allocation x at prices p.

Accepted Answer

If everyone likes their bundle in allocation y better than x, then they are willing to pay more for it. This indicates that the total value of allocation y at prices p exceeds the total value of allocation x at prices p, making allocation y a preferred competitive equilibrium.

Question 10

If the initial endowment is on the contract curve, then there must always be a competitive equilibrium in which no trade takes place.

Accepted Answer

If the initial endowment is on the contract curve, it means that any feasible allocation that could benefit one person cannot occur without harming another person. Therefore, there would be no opportunity for mutually beneficial trade and the competitive equilibrium would involve no trade.

Question 11

The second welfare theorem of economics states that if preferences are convex, then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.

Accepted Answer

The second welfare theorem of economics does indeed state that if preferences are convex, then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.

Question 12

In general equilibrium analysis, an allocation is a feasible allocation if every consumer is consuming a bundle that costs no more than his or her income.

Accepted Answer

The answer of In general equilibrium analysis, an allocation is...

Question 13

A competitive equilibrium allocation must be a feasible allocation.

Accepted Answer

A competitive equilibrium allocation requires that all goods and resources are allocated in a way that satisfies all constraints and is feasible. This means that the quantity of each good consumed by all individuals cannot exceed the total quantity produced in the economy. Thus, a competitive equilibrium allocation must be a feasible allocation.

Question 14

Every allocation on the contract curve is Pareto optimal.

Accepted Answer

The contract curve represents the set of Pareto efficient allocations, meaning that every allocation on the curve cannot be improved for one party without making the other party worse off. Therefore, every allocation on the contract curve is Pareto optimal.

Question 15

If two people have identical Cobb-Douglas utility functions, then in every Pareto optimal allocation, they must consume all goods in the same proportions as each other.

Accepted Answer

In an allocation that is Pareto optimal, the marginal rate of substitution (MRS) between any two goods must be equal for both individuals. In the case of identical Cobb-Douglas utility functions, the MRS is fixed and only depends on the relative prices of the goods. Therefore, both individuals must consume all goods in the same proportions to maximize their utility given the prices of the goods.

Question 16

Jack Spratt's utility function is U(F, L) = L. His wife's utility function is U(F, L) = F. If Jack's initial endowment is 100 units of F and 50 units of L and if Jack's wife's initial endowment is 60 units of F and 100 units of L, then in an Edgeworth box for Jack and his wife, an allocation of F and L will be Pareto optimal only if it is at a corner of the box.

Accepted Answer

The answer of Jack Spratt's utility function is U(F, L)...

Question 17

If the assumptions of the first theorem of welfare economics apply and if the economy is in a competitive equilibrium, then any reallocation that benefits someone must harm someone else.

Accepted Answer

The answer of If the assumptions of the first theorem...

Question 18

In a pure exchange economy with two goods, if there is a competitive equilibrium with prices p₁ = $12 and p₂ = $27, then there must also be a competitive equilibrium with prices p₁ = $24 and p₂ = $54.

Accepted Answer

This statement follows from the double auction market clearing condition, which requires that the total demand for each good equals its total supply. If the competitive equilibrium prices p₁ = $12 and p₂ = $27 clear the market, then the total demand for each good must be equal to the total supply. If we double the prices to $24 and $54, the quantity demanded for each good will decrease, and the quantity supplied will increase according to the law of supply and demand. However, the equilibrium condition still holds because the demand and supply for each good will adjust until they are equal at the new prices. Therefore, there must also be a competitive equilibrium with prices p₁ = $24 and p₂ = $54.

Question 19

Jack Spratt's utility function is U(F, L) = L. His wife's utility function is U(F, L) = F. If Jack's initial endowment is 10 units of F and 5 units of L and if Jack's wife's initial endowment is 6 units of F and 10 units of L, then in an Edgeworth box for Jack and his wife, an allocation of F and L will be Pareto optimal only if it is at a corner of the box.

Accepted Answer

The answer of Jack Spratt's utility function is U(F, L)...

Question 20

If demand varies continuously with price, then even if there are thousands of goods, there will be at least one set of prices such that demand equals supply in every market.

Accepted Answer

This statement is based on the principle of the law of supply and demand, which states that as price increases, demand decreases and supply increases, and vice versa. Therefore, if demand varies continuously with price, there will always be a set of prices where the market equilibrium is reached, with demand equal to supply. This holds true for all types of goods and markets, regardless of the number of goods involved.

Quiz 30: Exchange

If there are consumption externalities, then a competitive equilibrium is not necessarily Pareto optimal.

A pure exchange economy is an economy where goods are traded but there is no production.

In a competitive pure exchange economy, if the total value of excess demand for all types of food is zero, then the total value of excess demand for all nonfood commodities must be zero.

If two people have identical homothetic preferences and if their indifference curves have a diminishing marginal rate of substitution, then in an Edgeworth box, the locus of Pareto optimal allocations between them is a diagonal straight line.

In a model with two consumers, two goods, and no production, the contract curve must be a line going from one consumer's origin to the other consumer's origin.

Partial equilibrium analysis concerns only supply or only demand while general equilibrium analysis deals with supply and demand at the same time.

From Walras's law it follows that in a market with two goods, if demand equals supply in one market, then demand must equal supply in the other market.

If allocation x is a competitive equilibrium at prices p and if everybody likes his bundle in allocation y better than his bundle in allocation x, then the total value of allocation y at prices p exceeds the total value of allocation x at prices p.

If the initial endowment is on the contract curve, then there must always be a competitive equilibrium in which no trade takes place.

The second welfare theorem of economics states that if preferences are convex, then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.

In general equilibrium analysis, an allocation is a feasible allocation if every consumer is consuming a bundle that costs no more than his or her income.

A competitive equilibrium allocation must be a feasible allocation.

Every allocation on the contract curve is Pareto optimal.

If two people have identical Cobb-Douglas utility functions, then in every Pareto optimal allocation, they must consume all goods in the same proportions as each other.

If the assumptions of the first theorem of welfare economics apply and if the economy is in a competitive equilibrium, then any reallocation that benefits someone must harm someone else.

In a pure exchange economy with two goods, if there is a competitive equilibrium with prices p1 = $12 and p2 = $27, then there must also be a competitive equilibrium with prices p1 = $24 and p2 = $54.

If demand varies continuously with price, then even if there are thousands of goods, there will be at least one set of prices such that demand equals supply in every market.

In a pure exchange economy with two goods, if there is a competitive equilibrium with prices p₁ = $12 and p₂ = $27, then there must also be a competitive equilibrium with prices p₁ = $24 and p₂ = $54.