Chapter 16: General Equilibrium and Economic Efficiency

255

PART IV

INFORMATION, MARKET FAILURE,

AND THE ROLE OF GOVERNMENT

CHAPTER 16

GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY

QUESTIONS FOR REVIEW

1. Why can feedback effects make a general equilibrium analysis substantially different

from a partial equilibrium analysis?

A partial equilibrium analysis focuses on the interaction of supply and demand for

one market. It ignores the influences that shifts in supply and demand in one

market might have on the markets for complements and substitutes. A general

equilibrium analysis takes feedback effects into account, where a price or quantity

adjustment in one market can cause a price or quantity adjustment in related

markets. Ignoring these feedback effects can lead to inaccurate forecasts of the

full effect of changes in either supply or demand. An initial shift in demand in one

market, for example, can cause a shift in demand in a related market, which can

then cause a second shift in demand in the first market. A partial equilibrium

analysis will stop at the first initial shift whereas a general equilibrium analysis will

continue on and look at possible shifts in demand in related markets. Although

analysis should incorporate all feedback effects, one task of the economist is to

determine the markets that are most closely related to the market of primary

Chapter 16: General Equilibrium and Economic Efficiency

256

concern. Attention is directed toward these markets, thus enabling better forecasts

of changes in equilibrium prices and quantities.

2. In the Edgeworth box diagram, explain how one point can simultaneously represent the

market baskets owned by two consumers.

The Edgeworth box diagram allows us to represent the distribution of two goods

between two individuals. The box is formed by inverting the indifference curves

of one individual and superimposing these on the indifference curves of another

individual. The sides of the box represent the total amounts of the two goods

available to consumers. On the vertical axis, we read off the amount to each

individual as the difference between the horizontal axis and the point. For one

individual, this is the distance from the bottom of the box to the top, and for the

other, this is the distance from the top of the box to the bottom. Similarly, the

horizontal axis represents amounts of a second good distributed to the two

individuals. Each point in the box represents a different allocation of the two

goods between the two individuals.

3. In the analysis of exchange using the Edgeworth box diagram, explain why both

consumers’ marginal rates of substitution are equal at every point on the contract curve.

The contract curve, in the context of an Edgeworth box diagram, is the set of points

where the indifference curves of the two individuals are tangent. We know that

the marginal rate of substitution is equal to the (negative) slope of the indifference

curves. Also, when two curves are tangent at a point, their slopes are equal at that

point. Thus, by defining the contract curve as a set of indifference curve

tangencies, the marginal rates of substitution between the two goods are equal for

the two individuals given we assume convex indifference curves.

4. “Since all points on a contract curve are efficient, they are all equally desirable from a

social point of view.” Do you agree with this statement? Explain.

Chapter 16: General Equilibrium and Economic Efficiency

257

If society is only concerned with efficiency and not with equity, then all points on

the contract curve are equally desirable. Since it is impossible to make

comparisons of utility between individuals, economics focuses on efficiency. But,

if we are also concerned with equity (i.e., whether the final allocation is fair), then

all points on the contract curve are not equally desirable.

5. How does the utility possibilities frontier relate to the contract curve?

Since each point in an Edgeworth box can be compared to every other point by each

individual, individuals can assign a preference ordering to all points. This

preference ordering is the utility function. We can graph these preferences with

levels of satisfaction (utility) for one individual on one axis and levels of

satisfaction for a second individual on the other axis. (Of course, more than two

individuals can be represented with more axes.) The utility-possibility frontier

shows the levels of satisfaction achieved by each of two individuals when they have

traded to an efficient outcome on the contract curve. While points that lie between

the origin and the utility-possibility frontier are feasible they are not efficient

because further trading will leave one individual better off without making the other

individual worse off. Points outside the frontier are not feasible unless the

individuals are given greater amounts of one or both goods.

6. In the Edgeworth production box diagram, what conditions must hold for an allocation

to be on the production-contract curve? Why is a competitive equilibrium on the contract

curve?

When constructing an Edgeworth box for the production of two goods with two

inputs, each point in the box represents an allocation of the two inputs between the

two production processes. With production, each point can be ordered according

to the total output. These points lie on isoquants instead of on indifference curves.

Since each point simultaneously represents the allocation of inputs to two

production processes, it lies on two isoquants, one for each production process.

Chapter 16: General Equilibrium and Economic Efficiency

258

The production contract curve represents all combinations of inputs that are

technically efficient. Thus, there would be no way to increase the output of one

good without decreasing the output of the other good.

A competitive equilibrium is one point on the production-contract curve. It is the

intersection of the production-contract curve and a line passing through the initial

allocation with a slope equal to the ratio of prices. (The ratio of prices dictates the

rates at which inputs can be traded in the market.) For a competitive equilibrium

to hold, each producer must use inputs so that the slopes of the isoquants are equal

to one another and also equal to the ratio of the prices of the two inputs.

Therefore, the competitive equilibrium is efficient in production. (This

equilibrium assumes convex indifference curves.)

7. How is the production-possibilities frontier related to the production contract curve?

We can graph the quantities of each good produced (each point in the Edgeworth

box) on a two-dimensional graph, where the vertical axis represents the output of

one good and the horizontal axis represents the output of the other good. The

production-contract curve is represented in this two-dimensional graph as the

production possibilities frontier. Points inside this frontier are feasible but

inefficient. Points outside the frontier are infeasible and only attainable when more

inputs become available or production processes become more efficient. Points on

the production-possibilities frontier are the same as those on the production-contract

curve. The difference is that the production-contract curve measures inputs on the

axes and the production-possibilities frontier measures outputs on the axes.

8. What is the marginal rate of transformation (MRT)? Explain why the MRT of one

good for another is equal to the ratio of the marginal costs of producing the two goods.

The marginal rate of transformation, MRT, is equal to the absolute value of the

slope of the production possibilities frontier, and measures how much of one output

Chapter 16: General Equilibrium and Economic Efficiency

259

must be given up to produce one more unit of the other output. The total cost of

all inputs is the same at each point on the production possibilities frontier because

we use the same total amount of all inputs, and merely allocate them differently

along the frontier. Therefore, when we move down along the frontier, the cost of

producing one output is reduced by the same amount that the cost of producing the

other output is increased. Suppose the MRT is 4 in absolute value terms, then we

must give up 4 units of the output on the vertical axis to get one more unit of output

on the horizontal axis. This means that the total cost of producing the 4 units is the

same as the total cost of producing the one unit, or that the marginal cost of the

good on the horizontal axis is 4 times the marginal cost of the good on the vertical

axis.

9. Explain why goods will not be distributed efficiently among consumers if the MRT is not

equal to the consumers’ marginal rate of substitution.

If the marginal rate of transformation, MRT, is not equal to the marginal rate of

substitution, MRS, we could reallocate inputs in producing output to leave the

consumers and producers better off. If the MRS is greater than the MRT then

consumers are willing to pay more for another unit of a good than it will cost the

producers to produce another unit of the good. Both can therefore be made

better off by arranging a trade somewhere between what consumers are willing to

pay and what the producers have to pay to produce the extra unit. Note also that

when MRT

≠

MRS, the ratio of marginal cost will not be equal to the ratio of

prices. This means that one good is being sold at a price below marginal cost

and one good is being sold at a price above marginal cost. We should increase

the output of the one good whose price is above marginal cost and reduce the

output of the other good whose price is below marginal cost.

10. Why can free trade between two countries make consumers of both countries better off?

255

PART IV

INFORMATION, MARKET FAILURE,

AND THE ROLE OF GOVERNMENT

CHAPTER 16

GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY

QUESTIONS FOR REVIEW

1. Why can feedback effects make a general equilibrium analysis substantially different

from a partial equilibrium analysis?

A partial equilibrium analysis focuses on the interaction of supply and demand for

one market. It ignores the influences that shifts in supply and demand in one

market might have on the markets for complements and substitutes. A general

equilibrium analysis takes feedback effects into account, where a price or quantity

adjustment in one market can cause a price or quantity adjustment in related

markets. Ignoring these feedback effects can lead to inaccurate forecasts of the

full effect of changes in either supply or demand. An initial shift in demand in one

market, for example, can cause a shift in demand in a related market, which can

then cause a second shift in demand in the first market. A partial equilibrium

analysis will stop at the first initial shift whereas a general equilibrium analysis will

continue on and look at possible shifts in demand in related markets. Although

analysis should incorporate all feedback effects, one task of the economist is to

determine the markets that are most closely related to the market of primary

Chapter 16: General Equilibrium and Economic Efficiency

256

concern. Attention is directed toward these markets, thus enabling better forecasts

of changes in equilibrium prices and quantities.

2. In the Edgeworth box diagram, explain how one point can simultaneously represent the

market baskets owned by two consumers.

The Edgeworth box diagram allows us to represent the distribution of two goods

between two individuals. The box is formed by inverting the indifference curves

of one individual and superimposing these on the indifference curves of another

individual. The sides of the box represent the total amounts of the two goods

available to consumers. On the vertical axis, we read off the amount to each

individual as the difference between the horizontal axis and the point. For one

individual, this is the distance from the bottom of the box to the top, and for the

other, this is the distance from the top of the box to the bottom. Similarly, the

horizontal axis represents amounts of a second good distributed to the two

individuals. Each point in the box represents a different allocation of the two

goods between the two individuals.

3. In the analysis of exchange using the Edgeworth box diagram, explain why both

consumers’ marginal rates of substitution are equal at every point on the contract curve.

The contract curve, in the context of an Edgeworth box diagram, is the set of points

where the indifference curves of the two individuals are tangent. We know that

the marginal rate of substitution is equal to the (negative) slope of the indifference

curves. Also, when two curves are tangent at a point, their slopes are equal at that

point. Thus, by defining the contract curve as a set of indifference curve

tangencies, the marginal rates of substitution between the two goods are equal for

the two individuals given we assume convex indifference curves.

4. “Since all points on a contract curve are efficient, they are all equally desirable from a

social point of view.” Do you agree with this statement? Explain.

Chapter 16: General Equilibrium and Economic Efficiency

257

If society is only concerned with efficiency and not with equity, then all points on

the contract curve are equally desirable. Since it is impossible to make

comparisons of utility between individuals, economics focuses on efficiency. But,

if we are also concerned with equity (i.e., whether the final allocation is fair), then

all points on the contract curve are not equally desirable.

5. How does the utility possibilities frontier relate to the contract curve?

Since each point in an Edgeworth box can be compared to every other point by each

individual, individuals can assign a preference ordering to all points. This

preference ordering is the utility function. We can graph these preferences with

levels of satisfaction (utility) for one individual on one axis and levels of

satisfaction for a second individual on the other axis. (Of course, more than two

individuals can be represented with more axes.) The utility-possibility frontier

shows the levels of satisfaction achieved by each of two individuals when they have

traded to an efficient outcome on the contract curve. While points that lie between

the origin and the utility-possibility frontier are feasible they are not efficient

because further trading will leave one individual better off without making the other

individual worse off. Points outside the frontier are not feasible unless the

individuals are given greater amounts of one or both goods.

6. In the Edgeworth production box diagram, what conditions must hold for an allocation

to be on the production-contract curve? Why is a competitive equilibrium on the contract

curve?

When constructing an Edgeworth box for the production of two goods with two

inputs, each point in the box represents an allocation of the two inputs between the

two production processes. With production, each point can be ordered according

to the total output. These points lie on isoquants instead of on indifference curves.

Since each point simultaneously represents the allocation of inputs to two

production processes, it lies on two isoquants, one for each production process.

Chapter 16: General Equilibrium and Economic Efficiency

258

The production contract curve represents all combinations of inputs that are

technically efficient. Thus, there would be no way to increase the output of one

good without decreasing the output of the other good.

A competitive equilibrium is one point on the production-contract curve. It is the

intersection of the production-contract curve and a line passing through the initial

allocation with a slope equal to the ratio of prices. (The ratio of prices dictates the

rates at which inputs can be traded in the market.) For a competitive equilibrium

to hold, each producer must use inputs so that the slopes of the isoquants are equal

to one another and also equal to the ratio of the prices of the two inputs.

Therefore, the competitive equilibrium is efficient in production. (This

equilibrium assumes convex indifference curves.)

7. How is the production-possibilities frontier related to the production contract curve?

We can graph the quantities of each good produced (each point in the Edgeworth

box) on a two-dimensional graph, where the vertical axis represents the output of

one good and the horizontal axis represents the output of the other good. The

production-contract curve is represented in this two-dimensional graph as the

production possibilities frontier. Points inside this frontier are feasible but

inefficient. Points outside the frontier are infeasible and only attainable when more

inputs become available or production processes become more efficient. Points on

the production-possibilities frontier are the same as those on the production-contract

curve. The difference is that the production-contract curve measures inputs on the

axes and the production-possibilities frontier measures outputs on the axes.

8. What is the marginal rate of transformation (MRT)? Explain why the MRT of one

good for another is equal to the ratio of the marginal costs of producing the two goods.

The marginal rate of transformation, MRT, is equal to the absolute value of the

slope of the production possibilities frontier, and measures how much of one output

Chapter 16: General Equilibrium and Economic Efficiency

259

must be given up to produce one more unit of the other output. The total cost of

all inputs is the same at each point on the production possibilities frontier because

we use the same total amount of all inputs, and merely allocate them differently

along the frontier. Therefore, when we move down along the frontier, the cost of

producing one output is reduced by the same amount that the cost of producing the

other output is increased. Suppose the MRT is 4 in absolute value terms, then we

must give up 4 units of the output on the vertical axis to get one more unit of output

on the horizontal axis. This means that the total cost of producing the 4 units is the

same as the total cost of producing the one unit, or that the marginal cost of the

good on the horizontal axis is 4 times the marginal cost of the good on the vertical

axis.

9. Explain why goods will not be distributed efficiently among consumers if the MRT is not

equal to the consumers’ marginal rate of substitution.

If the marginal rate of transformation, MRT, is not equal to the marginal rate of

substitution, MRS, we could reallocate inputs in producing output to leave the

consumers and producers better off. If the MRS is greater than the MRT then

consumers are willing to pay more for another unit of a good than it will cost the

producers to produce another unit of the good. Both can therefore be made

better off by arranging a trade somewhere between what consumers are willing to

pay and what the producers have to pay to produce the extra unit. Note also that

when MRT

≠

MRS, the ratio of marginal cost will not be equal to the ratio of

prices. This means that one good is being sold at a price below marginal cost

and one good is being sold at a price above marginal cost. We should increase

the output of the one good whose price is above marginal cost and reduce the

output of the other good whose price is below marginal cost.

10. Why can free trade between two countries make consumers of both countries better off?

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