Equilibrium and Efficiency
We have now analyzed market trade in a pure exchange model. This gives us a specific model of trade that we can compare to the general model of trade that we discussed in the beginning of this chapter. One question that might arise about the use of a competitive market is whether this mechanism can really exhaust all of the gains from trade. After we have traded to a competitive equilibrium where demand equals supply in every market, will there be any more trades that people will desire to...
Production Possibilities
We have now seen how production and consumption decisions can be made in a one-input, one-output economy. In this section we want to explore how this model can be generalized to an economy with several inputs and outputs. Although we will deal only with the two-good case, the concepts will generalize naturally to many goods. So let us suppose that there is some other good that Robinson might produce say fish. He can devote his time to gathering coconuts or to fishing. In Figure 32.7 we have...
qi Piyi xi 0
This equation says that the change in the quantity demanded must have the opposite sign from that of the price change, which is what we wanted to show. The total change in demand is still equal to the substitution effect plus the income effect but now it is the Hicks substitution effect. Since the Hicks substitution effect is also negative, the Slutsky equation takes exactly the same form as we had earlier and has exactly the same interpretation. Both the Slutsky and Hicks definitions of the...
nomothetic Preferences
All of the ineostQ offer curves and Enge curves that we have seen up to now have been straightforward in fact they've been straight lines This has happened becaose oar examples have been so simple. Heal Enge curves do not have to be straight lines. In general, when income goes up, the demand for a good cotild increase more or less rapidly than income increases. If the demand for a good goes up by a greater proportion than income, we say that it is a luxury good, and if Itgoesup by a lesser...
Review Questions Pdz
1. If two goods are perfect substitutes, what is the demand function for good 2 2. Suppose that indifference curves are described by straight lines with a slope of 6. Given arbitrary prices and money income pi, p2, and m, what will the consumer's optimal choices look like 3. Suppose that a consumer always consumes 2 spoons of sugar with each cup of coffee. If the price of sugar is p per spoonful and the price of coffee is p2 per cup and the consumer has m dollars to spend on coffee and sugar,...
Review Questions
1. Originally the consumer faces the budget line p Xi P2 2 n. Then the price of good 1 doubles, the price of good 2 becomes 8 times larger, and income becomes 4 times larger. Write down an equation for the new budget line in terms of the original prices and income. 2. What happens to the budget line if the price of good 2 increases, but the price of good 1 and income remain constant 3. If the price of good 1 doubles and the price of good 2 triples, does the budget line become flatter or steeper...
Summary Sjj
1. Public goods are goods for which everyone must consume the same amount, such as national defense, air pollution, and so on. 2. If a public good is to be provided in some fixed amount or not provided at all, then a necessary and sufficient condition for provision to be Pareto efficient is that the sum of the willingnesses to pay the reservation prices exceeds the cost of the public good. 3. If a public good can be provided in a variable amount, then the necessary condition for a given amount...
The Market for Lemons
Let us look at a model of a market where the demanders and suppliers have different information about the qualities of the goods being sold.1 Consider a market with 100 people who want to sell their used cars and 100 people who want to buy a used car. Everyone knows that 50 of the cars are plums and 50 are lemons.2 The current owner of each car knows its quality, but the prospective purchasers don't know whether any given car is a plum or a lemon. The owner of a lemon is willing to part with it...
Voting
Private provision of a public good doesn't work very well, but there are several other mechanisms for social choice. One of the most common mechanisms in democratic countries is voting. Let's examine how well it works for the provision of public goods. Voting isn't very interesting in the case of two consumers, so we will suppose that we have n consumers. Furthermore, so as not to worry about ties, we'll suppose that n is an odd number. Let's imagine that the consumers are voting about the size...
Slutsky Equation
Economists often are concerned with how a consumer's behavior changes in response to changes in the economic environment. The case we want to consider in this chapter is how a consumer's choice of a good responds to changes in its price. It is natural to think that when the price of a good rises the demand for it will fall. However, as we saw in Chapter 6 it is possible to construct examples where the optimal demand for a good decreases when its price falls. A good that has this property is...
Quasilinear Preferences and the Coase Theorem
We argued above that as long as property rights were well defined, trade between agents would result in an efficient allocation of the externality. In general, the amount of the externality that will be generated in the efficient solution will depend on the assignment of property rights. In the case of the two roommates, the amount of smoke generated will depend on whether the smoker has the property rights or the nonsmoker has them. QUASILINEAR PREFERENCES AND THE COASE THEOREM 631 But there...
Review Questions Bmv
1. The competitive price of coconuts is 6 per pound and the price of fish is 3 per pound. If society were to give up 1 pound of coconuts, how many more pounds of fish could be produced 2. What would happen if the firm depicted in Figure 32.2 decided to pay a higher wage 3. In what sense is a competitive equilibrium a good or bad thing for a given economy 4. If Robinson's marginal rate of substitution between coconuts and fish is 2 and the marginal rate of transformation between the two goods is...
AT1 Second derivatives
The second derivative of a function is the derivative of the derivative of that function, if f x , the second derivative of f x with respect to x is written as tPf amp dx2 or f x . We know that The second derivative measures the curvature of a function. A function with a negative second derivative at some point is concave near that point its slope is decreasing. A function with a positive second derivative at a point is convex aesr that point its slope is increasing. A function with a zero se...
Quasilinear Preferences and Public Goods
In general, the optimal amount of the public good will be different at different allocations of the private good. But if the consumers have quasilinear preferences it turns out that there will be a unique amount of the public good supplied at every efficient allocation. The easiest way to see this is to think about the kind of utility function that represents quasilinear preferences. As we saw in Chapter 4, quasilinear preferences have a utility representation of the form Ui x G X Vj G . This...
Problems with the Clarke Tax
Despite the nice features of the Clarke tax it does have some problems. The first problem is that it only works with quasilinear preferences. This is because we can't have the amount that you have to pay influence your demand for the public good. It is important that there is a unique optimal level of the public good. The second problem is that the Clarke tax doesn't really generate a Pareto efficient outcome. The level of the public good will be optimal, but the private consumption could be...
Individualistic Social Welfare Functions
Up until now we have been thinking of individual preferences as being defined over entire allocations rather than over each individual's bundle of goods. But, as we remarked earlier, individuals might only care about their own bundles. In this case, we can use Xi to denote individual i's consumption bundle, and let Ui xi be individual i's utility level using some fixed representation of utility. Then a social welfare function will The welfare function is directly a function of the individuals'...
Market Dynamics
Which of the three equilibria will we see occur So far the model gives us no reason to choose among them. At each of these equilibria, demand equals supply. However, we can add a dynamic adjustment process to help us decide which equilibrium is more likely to occur. It is plausible to assume that when people are willing to pay more than the cost of the good, the size of the market expands and, when they are willing to pay less, the market contracts. Geometrically this is saying that when the...
Moral Hazard and Adverse Selection
Moral hazard refers to situations where one side of the market can't observe the actions of the other. For this reason it is sometimes called a hidden action problem. Adverse selection refers to situations where one side of the market can't observe the type or quality of the goods on other side of the market. For this reason it is sometimes called a hidden information problem. Equilibrium in a market involving hidden action typically involves some form of rationing firms would like to provide...
Smokers and Nonsmokers
It is convenient to start with an example to illustrate some of the main considerations. We'll imagine two roommates, A and B, who have preferences over money and smoke. We suppose that both consumers like money, but that A likes to smoke and B likes clean air. We can depict the consumption possibilities for the two consumers in an Edge worth box. The length of the horizontal axis will represent the total amount of money the two agents have, and the height of the vertical axis will represent...
pxtxpxA
This statement says that the bundle chosen at year b is revealed preferred to the bundle chosen at year t. This analysis implies that if the Paasche price index is greater than the expenditure index, then the consumer must be better off in year b than in year t. This is quite intuitive. After all, if prices rise by more than income rises in the movement from i gt to i, we would expect that would tend to make the consumer worse off. The revealed preference analysis given above confirms this...
Review Questions 1
1. If we observe a consumer choosing x 1,2 2 when yi,y2 is available one time, are we justified in concluding that 1,0 2 2 1 2 2 2. Consider a group of people A, B, C and the relation at least as tall as, as in A is at least as tall as B. Is this relation transitive Is it complete 3. Take the same group of people and consider the relation strictly taller than. Is this relation transitive Is it reflexive Is it complete 4. A college football coach says that given any two linemen A and B, he...
x mp1
The case of perfect complements is illustrated in Figure 5.6. Note that the optimal choice must always lie on the diagonal, where the consumer is purchasing equal amounts of both goods, no matter what the prices are. In terms of our example, this says that people with two feet buy shoes in pairs.2 Let us solve for the optimal choice algebraically. We know that this consumer is purchasing the same amount of good 1 and good 2, no matter what the prices. Let this amount be denoted by x. Then we...
The marginal rate of substitution MRS The marginal rate of substitution
The marginal rate of substitution measures an interesting aspect of the consumer's behavior. Suppose that the consumer has well-behaved preferences, that is, preferences that are monotonic and convex, and that he is currently consuming some bundle xi, - We now will offer him a trade he can exchange good 1 for 2, or good 2 for 1, in any amount at a rate of exchange of E. That is, if the consumer gives up Ax units of good 1, he can get EAxi units of good 2 in exchange. Or, conversely, if he gives...
Summary 1
1. The budget set consists of all bundles of goods that the consumer can afford at given prices and income. We will typically assume that there are only two goods, but this assumption is more general than it seems. 2. The budget line is written as p X P2X2 wi- ft has a slope of pi p2, a vertical intercept of m p2, and a horizontal intercept of m pi. 3. Increasing income shifts the budget line outward. Increasing the price of good 1 makes the budget line steeper. Increasing the price of good 2...
Comparative Statics of Labor Supply
First let us consider how a consumer's labor supply changes as money income changes with the price and wage held fixed. If you won the state Labor supply. The optimal choice describes the demand for leisure measured from the origin to the right, and the supply of labor measured from the endowment to the left. lottery and got a big increase in nonlabor income, what would happen to your supply of labor What would happen to your demand for leisure For most people, the supply of labor would drop...
Summary
1. Economics proceeds by making models of social phenomena, which are simplified representations of reality. 2. In this task, economists are guided by the optimization principle, which states that people typically try to choose what's best for them, and by the equilibrium principle, which says that prices will adjust until demand and supply are equal. 3. The demand curve measures how much people wish to demand at each price, and the supply curve measures how much people wish to supply at each...
Quasilinear Preferences 1
Another kind of preferences that generates a special form of income offer curves and Engel curves is the case of quasilinear preferences. Recall the definition of quasilinear preferences given in Chapter 4. This is the case where all indifference curves are shifted versions of one indifference curve as in Figure 6.8. Equivalently, the utility function for these preferences takes the form u x 1, 2 v xi x2. What happens if we shift the budget line outward In this case, if an indifference curve is...
Review Questions Jmb
1. If a consumer's net demands are 5,-3 and her endowment is 4,4 , what are her gross demands 2. The prices are i gt i,P2 2,3 , and the consumer is currently consuming x ,X2 4,4 . There is a perfect market for the two goods in which they can be bought and sold costlessly. Will the consumer necessarily prefer consuming the bundle yi,y2 3,5 Will she necessarily prefer having the bundle 2 1,2 2 3. The prices are 1, 2 2,3 , and the consumer is currently consuming xi,x2 4,4 . Now the prices change...
Perfect Substitutes Pch
The offer curve and demand curve for perfect substitutes the red and blue pencils example are illustrated in Figure 6.12. As we saw in Chapter 5, the demand for good 1 is zero when pi gt p2, any amount on the budget line when pi p2, and m pi when pi lt p2. The offer curve traces out these possibilities. In order to find the demand curve, we fix the price of good 2 at some price p and graph the demand for good 1 versus the price of good 1 to get the shape depicted in Figure 6.12B.
Perfect Substitutes 1
The case of perfect substitutes is illustrated in Figure 5.5. We have three possible cases. If p2 gt Pi, then the slope of the budget line is flatter than the slope of the indifference curves. In this case, the optimal bundle is where the consumer spends all of his or her money on good 1. If p gt p2, then the consumer purchases only good 2. Finally, if p P2, there is a whole range of optimal choices any amount of goods 1 and 2 that satisfies the budget constraint is optimal in this case. Thus...
Various kinds of preferences Panel A depicts convex preferences panel B depicts
Can you think of preferences that are not convex One possibility might be something like my preferences for ice cream and olives. I like ice cream and I like olives but I don't like to have them together In considering my consumption in the next hour, I might be indifferent between consuming 8 ounces of ice cream and 2 ounces of olives, or 8 ounces of olives and 2 ounces of ice cream. But either one of these bundles would be better than consuming 5 ounces of each These are the kind of...
Perfect Complements
This is the left shoe-right shoe case. In these preferences the consumer only cares about the number of pairs of shoes he has, so it is natural to choose the number of pairs of shoes as the utility function. The number of complete pairs of shoes that you have is the minimum of the number of right shoes you have, Xi, and the number of left shoes you have, x2. Thus the utility function for perfect complements takes the form w xi,x2 min x ,x2 . To verify that this utility function actually works,...
Comparative Statics
Now that we have an economic model of the apartment market, we can begin to use it to analyze the behavior of the equilibrium price. For example, we can ask how the price of apartments changes when various aspects of the market change. This kind of an exercise is known as comparative statics, because it involves comparing two static equilibria without worrying about how the market moves from one equilibrium to another. The movement from one equilibrium to another can take a substantial amount...
Market Equilibrium
We now have a way of representing the demand and the supply side of the apartment market. Let us put them together and ask what the equilibrium behavior of the market is. We do this by drawing both the demand and the supply curve on the same graph in Figure 1.4. In this graph we have used p to denote the price where the quantity of apartments demanded equals the quantity supplied. This is the equilibrium price of apartments. At this price, each consumer who is willing to pay at least p is able...
Kinky tastes Here is an optimal consumption bundle where the indifference curve
The second exception is more interesting. Suppose that the optimal point occurs where the consumption of some good is zero as in Figure 5.3. Then the slope of the indifference curve and the slope of the budget line are different, but the indifference curve still doesn't cross the budget line. We say that Figure 5.3 represents a boundary optimum, while a case like Figure 5.1 represents an interior optimum. If we are willing to rule out kinky tastes we can forget about the example given in Figure...
Perfect Complements Nhk
The case of perfect complements the right and left shoes example is depicted in Figure 6.13. We know that whatever the prices are, a consumer will demand the same amount of goods 1 and 2. Thus his offer curve will be a diagonal line as depicted in Figure 6.13A. We saw in Chapter 5 that the demand for good 1 is given by If we fix rn and p2 and plot the relationship between x and pi, we get the curve depicted in Figure 6.13B. A Price offer curve B Demand curve Perfect substitutes. Price offer...
Assumptions about Preferences
Economists usually make some assumptions about the consistency of consumers' preferences. For example, it seems unreasonable not to say contradictory to have a situation where xi, 2 1,2 2 and, at the same time, 2 1,2 2 gt - 1, 2 - For this would mean that the consumer strictly prefers the x-bundle to the y-bundle and vice versa. So we usually make some assumptions about how the preference relations work. Some of the assumptions about preferences are so fundamental that we can refer to them as...
Properties of the Budget Set
The budget line is the set of bundles that cost exactly m These are the bundles of goods that just exhaust the consumer's income. The budget set is depicted in Figure 2.1. The heavy line is the budget line the bundles that cost exactly m and the bundles below this line are those that cost strictly less than m. The budget set. The budget set consists of all bundles that are affordable at the given prices and income. We can rearrange the budget line in equation 2.3 to give us the formula This is...
The Slutsky Equation Revisited
The above applications of revealed preference are handy, but they don't really answer the main question how does the demand for a good react to a change in its price We saw in Chapter 8 that if money income was held constant, and the good was a normal good, then a reduction in its price must lead to an increase in demand. The catch is the phrase money income was held constant. The case we are examining here necessarily involves a change in money income, since the value of the endowment will...
WeilBehaved Preferences
We've now seen some examples of indifference curves. As we've seen, many kinds of preferences, reasonable or unreasonable, can be described by these simple diagrams. But if we want to describe preferences in general, it will be convenient to focus on a few general shapes of indifference curves. In 1 2 A Indifference curves 1 2 A Indifference curves A discrete good. Here good 1 is only available in integer amounts. In panel A the dashed lines connect together the bundles that are indifferent T...
Consumer Preferences
We will suppose that given any two consumption bundles, xi, 2 and 2 1,2 2 , the consumer can rank them as to their desirability. That is, the consumer can determine that one of the consumption bundles is strictly better than the other, or decide that she is indifferent between the two bundles. We will use the symbol gt - to mean that one bundle is strictly preferred to another, so that 1,22 2 1,2 2 should be interpreted as saying that the consumer strictly prefers x ,Z2 to 2 1,2 2 , in the...
AU MU2Ax2
It is important to realize that the magnitude of marginal utility depends on the magnitude of utility. Thus it depends on the particular way that we choose to measure utility. If we multiplied utility by 2, then marginal utility would also be multiplied by 2. We would still have a perfectly valid utility function in that it would represent the same preferences, but it would just be scaled differently. This means that marginal utility itself has no behavioral content. How can we calculate...
The Slutsky Equation and Intertemporal Choice
The Slutsky equation can be used to decompose the change in demand due to an interest rate change into income effects and substitution effects, just If a person is a lender and the interest rate rises, he or she will remain a lender. Increasing the interest rate pivots the budget line around the endowment to a steeper position revealed preference implies that the new consumption bundle must lie to the left of the endowment. as in Chapter 9. Suppose that the interest rate rises. What will be the...
Pareto Efficiency
One useful criterion for comparing the outcomes of different economic institutions is a concept known as Pareto efficiency or economic efficiency.1 We start with the following definition if we can find a way to make some people better off without making anybody else worse off, we have a Pareto improvement. If an allocation allows for a Pareto improvement, it is called Pareto inefficient if an allocation is such that no Pareto improvements are possible, it is called Pareto efficient. A Pareto...
Quasilinear preferences An income offer curve A and an Engel curve B with
What would be a real-life situation where this kind of thing might occur Suppose good 1 is pencils and good 2 is money to spend on other goods. Initially I may spend my income only on pencils, but when my income gets large enough, I stop buying additional pencils all of my extra income is spent on other goods. Other examples of this sort might be salt or toothpaste. When we are examining a choice between all other goods and some single good that isn't a very large part of the consumer's budget,...
Budget Line Changes
In the next chapter we will analyze how the consumer chooses an optimal consumption bundle from his or her budget set. But we can already state some observations here that follow from what we have learned about the movements of the budget line. First, we can observe that since the budget set doesn't change when we multiply all prices and income by a positive number, the optimal choice of the consumer from the budget set can't change either. Without even analyzing the choice process itself, we...
Income Offer Curves and Engel Curves
We have seen that an increase in income corresponds to shifting the budget line outward in a parallel manner. We can connect together the demanded bundles that we get as we shift the budget line outward to construct the income offer curve. This curve illustrates the bundles of goods that are demanded at the different levels of income, as depicted in Figure 6.3A. The income offer curve is also known as the income expansion path. If both goods are normal goods, then the income expansion path will...
How the Budget Line Changes
When prices and incomes change, the set of goods that a consumer can afford changes as well. How do these changes affect the budget set Let us first consider changes in income. It is easy to see from equation 2.4 that an increase in income will increase the vertical intercept and not affect the slope of the line. Thus an increase in income will result in a parallel shift outward of the budget line as in Figure 2.2. Similarly, a decrease in income will cause a parallel shift inward. Increasing...
Monopoly Behavior
Price Discrimination 445 First-Degree Price Discrimination 445 Example First-degree Price Discrimination in Practice Second-Degree Price Discrimination 448 Example Price Discrimination in Airfares Example Prescription Drug Prices Third-Degree Price Discrimination 452 Example Linear Demand Curves Example Calculating Optimal Price Discrimination Example Price Discrimination in Academic Journals Bundling 457 Example Software Suites Two-Part Tariffs 458 Monopolistic Competition 459 A Location Model...
Examples of Preferences
Let us try to relate preferences to indifference curves through some examples. We'll describe some preferences and then see what the indifference curves that represent them look like. Indifference curves cannot cross. If they did, X, Y, and Z would all have to be indifferent to each other and thus could not lie on distinct indifference curves. There is a general procedure for constructing indifference curves given a verbal'' description of the preferences. First plop your pencil down on the...