Question 1

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

Pareto optimality in an Edgeworth box does not require allocations to be at the corners of the box. Pareto optimal allocations occur along the contract curve, which represents allocations where the marginal rate of substitution between goods F and L is equal for both Jack and his wife, indicating no further mutually beneficial trades can be made. This curve does not necessarily lie at the corners of the box.

Question 2

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 is true based on the existence of the law of one price in competitive markets. If one equilibrium exists with prices (p1,q1) and another equilibrium exists with prices (p2,q2), then there must exist a third equilibrium with prices in between (p1,p2) and corresponding quantities that clear the market. Therefore, the given statement is true as the prices in the second equilibrium are between the prices in the first equilibrium.

Question 3

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 only looks at one side of the market, either supply or demand, while general equilibrium analysis takes into account both supply and demand and how they interact with each other in the overall economy.

Question 4

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 equivalent to the existence of a general equilibrium in the economy, which is a well-established result in the theory of competitive markets. Under certain assumptions, including continuous demand functions, the existence of a general equilibrium can be proven mathematically. This means that there is a set of prices for all goods such that all markets clear (i.e., demand equals supply) simultaneously.

Question 5

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 first theorem of welfare economics states that any competitive equilibrium leads to a Pareto efficient allocation, meaning no reallocation can make someone better off without making someone else worse off.

Question 6

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 a known result in microeconomics. When individuals have identical homothetic preferences and diminishing marginal rate of substitution, the Pareto optimal allocations lie along a 45-degree line (diagonal) in an Edgeworth box. This is due to the fact that the slope of the indifference curves for both individuals is the same, therefore the only way to improve one individual's utility is to decrease the other's. The Pareto optimal allocation is the point where both individuals' MRS are equal, which is on the diagonal line.

Question 7

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

Given that allocation x is a competitive equilibrium at prices p, it means that no one can be made better off without making someone else worse off. However, if everyone likes his bundle in allocation y better than his bundle in allocation x, it means that allocation y is a better allocation than allocation x. Therefore, the total value of allocation y at prices p exceeds the total value of allocation x at prices p.

Question 8

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

Pareto optimality in an Edgeworth box does not require that the allocation be at a corner of the box. Pareto optimal allocations occur along the contract curve, which represents allocations where the marginal rate of substitution between goods F and L is equal for both Jack and his wife. These allocations can occur anywhere along the contract curve, not just at the corners of the Edgeworth box.

Question 9

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

Accepted Answer

In a pure exchange economy, agents exchange goods and services with each other but do not engage in any production activities.

Question 10

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

This is the definition of Walras's law, which states that if there is market equilibrium in one market, then there must be market equilibrium in all other markets.

Question 11

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

This is a direct application of the First Welfare Theorem, which states that in a competitive equilibrium, the allocation of goods will be Pareto optimal and will also satisfy individual rationality (i.e. each person is at least as well off as they would be in a different allocation). Since the Cobb-Douglas utility function exhibits constant returns to scale and is quasi-concave, it satisfies the conditions for the existence of a competitive equilibrium. In such an equilibrium, the relative prices of goods will be equal to the marginal rates of substitution of each individual. Since the two individuals have identical utility functions, their marginal rates of substitution for goods will be identical as well, meaning that they will consume all goods in the same proportions in every Pareto optimal allocation.

Question 12

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

Accepted Answer

Consumption externalities occur when an individual's consumption affects the welfare of others, either positively or negatively. In such cases, the market may not take into account the full social cost or social benefit of consumption, and therefore a competitive equilibrium may not lead to a Pareto optimal outcome. This is because some individuals may consume more or less than the socially optimal level, leading to a suboptimal allocation of resources.

Question 13

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 represents an allocation that is Pareto efficient and all agents prefer it over any other feasible allocation. In a competitive equilibrium, prices adjust to ensure that demand equals supply in every market. Since the initial endowment already satisfies the market clearing condition and is Pareto efficient, there is no incentive for agents to trade further. Therefore, there exists a competitive equilibrium in which no trade takes place.

Question 14

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 "no goods left on the table" theorem, which states that in a competitive pure exchange economy, if the total value of excess demand for one set of goods is zero, then the total value of excess demand for all other sets of goods must also be zero. Therefore, 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 also be zero.

Question 15

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 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

Pareto optimality in an Edgeworth box does not require allocations to be at the corners of the box. Pareto optimal allocations occur along the contract curve, which represents allocations where the marginal rate of substitution between goods F and L is equal for both Jack and his wife, indicating no further mutually beneficial trades can be made. This curve does not necessarily lie at the corners of the box.

Question 17

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 18

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 in fact 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 19

Every allocation on the contract curve is Pareto optimal.

Accepted Answer

Pareto optimality occurs when no individual can be made better off without making someone else worse off. Every allocation on the contract curve meets this criteria, since it represents a point where both parties prefer the same allocation over any other possible allocation.

Question 20

A competitive equilibrium allocation must be a feasible allocation.

Accepted Answer

In a competitive equilibrium, all markets must clear, meaning that the quantity supplied equals the quantity demanded for every good or service. This implies that the allocation of resources is feasible. If the allocation were not feasible, it would not be possible for all markets to clear and achieve a competitive equilibrium.

Quiz 30: Exchange-Part A

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.