## Firm Supply

In this chapter we will see how to derive the supply curve of a competitive firm from its cost function using the model of profit maximization. The first thing we have to do is to describe the market environment in which the firm operates. Every firm faces two important decisions choosing how much it should produce and choosing what price it should set. If there were no constraints on a profit-maximizing firm, it would set an arbitrarily high price and produce an arbitrarily large amount of...

## Cobb Douglas Preferences

Another commonly used utility function is the Cobb-Douglas utility function where c and d are positive numbers that describe the preferences of the consumer.2 The Cobb-Douglas utility function will be useful in several examples. The preferences represented by the Cobb-Douglas utility function have the general shape depicted in Figure 4.5. In Figure 4.5A, we have illustrated the indifference curves for c 1 2, d 1 2. In Figure 4.5B, we have illustrated the indifference curves for c 1 5, d 4 5....

## As

This shows that the merged firm will take into account the effect of pollution on the marginal costs of both the steel firm and the fishery. When the steel division decides how much pollution to produce, it considers the effect of this action on the profits of the fish division that is, it takes the social cost of its production plan into account. What does this imply about the amount of pollution produced When the steel firm acted independently, the amount of...

## Inverse Demand and Supply Curves

We can look at market equilibrium in a slightly different way that is often useful. As indicated earlier, individual demand curves are normally viewed as giving the optimal quantities demanded as a function of the price charged. But we can also view them as inverse demand functions that measure the price that someone is willing to pay in order to acquire some given amount of a good. The same thing holds for supply curves. They can be viewed as measuring the quantity supplied as a function of...

## Implications of the Second Welfare Theorem

The Second Theorem of Welfare Economics asserts that under certain conditions, every Pareto efficient allocation can be achieved as a competitive equilibrium. What is the meaning of this result The Second Welfare Theorem implies that the problems of distribution and efficiency can be separated. Whatever Pareto efficient allocation you want can be supported by the market mechanism. The market mechanism is distributionally neutral whatever your criteria for a good or a just distribution of...

## Marginal Revenue Curves

We saw in the last section that marginal revenue is given by We will find it useful to plot these marginal revenue curves. First, note that when quantity is zero, marginal revenue is just equal to the price. For the first unit of the good sold, the extra revenue you get is just the price. But after that, the marginal revenue will be less than the price, since Ap Aq is negative. Think about it. If you decide to sell one more unit of output, you will have to decrease the price. But this reduction...

## Signaling

Recall our model of the used-car market the owners of the used cars knew the quality, but the purchasers had to guess at the quality. We saw that this asymmetric information could cause problems in the market in some cases, the adverse selection problem would result in too few transactions being made. However, the story doesn't end there. The owners of the good used cars have an incentive to try to convey the fact that they have a good car to the potential purchasers. They would like to choose...

## Implications of the First Welfare Theorem

The two theorems of welfare economics are among the most fundamental results in economics. We have demonstrated the theorems only in the simple Edgeworth box case, but they are true for much more complex models with arbitrary numbers of consumers and goods. The welfare theorems have profound implications for the design of ways to allocate resources. Let us consider the First Welfare Theorem. This says that any competitive equilibrium is Pareto efficient. There are hardly any explicit assump-...

## Inverse Factor Demand Curves

The factor demand curves of a firm measure the relationship between the price of a factor and the profit-maximizing choice of that factor. We saw above how to find the profit-maximizing choices for any prices, (p, w , w2), we just find those factor demands, (x*, ), such that the value of the marginal product of each factor equals its price. The inverse factor demand curve measures the same relationship, but from a different point of view. It measures what the factor prices must be for some...

## Framing Effects in Consumer Choice

In the basic model of consumer behavior, the choices were described in the abstract red pencils or blue pencils, hamburgers and french fries, and so on. However, in real life, people are strongly affected by how choices are presented to them or framed. A faded pair of jeans in a thrift shop may be perceived very differently than the same jeans sold in an exclusive store. The decision to buy a stock may feel quite different than the decision to sell a stock, even if both transactions end up with...

## First Degree Price Discrimination

Under first-degree price discrimination, or perfect price discrimination, each unit of the good is sold to the individual who values it most highly, at the maximum price that this individual is willing to pay for it. Consider Figure 25.1, which illustrates two consumers' demand curves for a good. Think of a reservation price model for demand where the individuals choose integer amounts of the goods and each step in the demand curve represents a change in the willingness to pay for additional...

## The Deadweight Loss of a

We've seen that taxing a good will typically increase the price paid by the demanders and decrease the price received by the suppliers. This certainly represents a cost to the demanders and suppliers, but from the economist's viewpoint, the real cost of the tax is that the output has been reduced. The lost output is the social cost of the tax. Let us explore the social cost of a tax using the consumers' and producers' surplus tools developed in Chapter 14. We start with the diagram given in...

## The Inverse Demand Function

We can look at the aggregate demand curve as giving us quantity as a function of price or as giving us price as a function of quantity. When we want to emphasize this latter view, we will sometimes refer to the inverse demand function, P(X). This function measures what the market price for good 1 would have to be for X units of it to be demanded. We've seen earlier that the price of a good measures the marginal rate of substitution (MRS) between it and all other goods that is, the price of a...

## Buying And Selling

In the simple model of the consumer that we considered in the preceding chapters, the income of the consumer was given. In reality people earn their income by selling things that they own items that they have produced, assets that they have accumulated, or, most commonly, their own labor. In this chapter we will examine how the earlier model must be modified so as to describe this kind of behavior. As before, we will limit ourselves to the two-good model. We now suppose that the consumer starts...

## Compensating and Equivalent Variation

The theory of consumer's surplus is very tidy in the case of quasilinear utility. Even if utility is not quasilinear, consumer's surplus may still be a reasonable measure of consumer's welfare in many applications. Usually the errors in measuring demand curves outweigh the approximation errors from using consumer's surplus. But it may be that for some applications an approximation may not be good enough. In this section we'll outline a way to measure utility changes without using consumer's...

## Returns to Scale

Now let's consider a different kind of experiment. Instead of increasing the amount of one input while holding the other input fixed, let's increase the Production function. This is a possible shape for a short-run production function. amount of all inputs to the production function. In other words, let's scale the amount of all inputs up by some constant factor for example, use twice as much of both factor 1 and factor 2. If we use twice as much of each input, how much output will we get The...

## Economics Cy Py

How do the maximum profits relate to producer's surplus In Figure 22.7 we see that producer's surplus the area to the left of the supply curve between a price of zero and a price of p will be a triangle with a base of y pj2 and a height of p. The area of this triangle is Comparing this with the profits expression, we see that producer's surplus equals profits plus fixed costs, as claimed. THE LONG-RUN SUPPLY CURVE OF A FIRM 395 A specific example of a supply curve. The supply curve and...

## Oligopoly

We have now investigated two important forms of market structure pure competition, where there are typically many small competitors, and pure monopoly, where there is only one large firm in the market. However, much of the world lies between these two extremes. Often there are a number of competitors in the market, but not so many as to regard each of them as having a negligible effect on price. This is the situation known as oligopoly. The model of monopolistic competition described in Chapter...

## Pareto Efficient Allocations

At the point M in this diagram the set of points above A's indifference curve doesn't intersect the set of points above B's indifference curve. The region where A is made better off is disjoint from the region where B is made better off. This means that any movement that makes one of the parties better off necessarily makes the other party worse off. Thus there are no exchanges that are advantageous for both parties. There are no mutually improving trades at...

## The Problem of Complements

To illustrate these points, let us consider the case of a Central Processing Unit (CPU) and an Operating System (OS). A CPU is an integrated 1 See Shapiro, Carl and Hal R. Varian, Information Rules A Strategic Guide to the Network Economy, Harvard Business School Press, 1998, for a guide to competitive circuit that is the brain of a computer. Two familiar manufacturers of CPUs are Intel and Motorola. An OS is the software that allows users and applications to access the functions of the CPU....

## Contingent Consumption

Since we now know all about the standard theory of consumer choice, let's try to use what we know to understand choice under uncertainty. The first question to ask is what is the basic thing that is being chosen The consumer is presumably concerned with the probability distribution of getting different consumption bundles of goods. A probability distribution consists of a list of different outcomes in this case, consumption bundles and the probability associated with each outcome. When a...

## The Numeraire

The budget line is defined by two prices and one income, but one of these variables is redundant. We could peg one of the prices, or the income, to some fixed value, and adjust the other variables so as to describe exactly the same budget set. Thus the budget line since the first budget line results from dividing everything by P2, and the second budget line results from dividing everything by m. In the first case, we have pegged p2 1, and in the second case, we have pegged m 1. Pegging the...

## Viyi iooi P2O2 50 222

Marginal revenue equals marginal cost in each market yields the two equations Solving we have 40 and y2 30. Substituting back into the inverse demand functions gives us the prices p 60 and p2 35. If the monopolist must charge the same price in each market, we first calculate the total demand D(p) Di(pi) + D2(p2) 200 - 3p. The inverse demand curve is Marginal revenue equals marginal cost gives us which can be solved to give y* 70 and p* 43 . In accord with the discussion in the previous section,...

## Perfect Complements

The demand behavior for perfect complements is shown in Figure 6.5. Since the consumer will always consume the same amount of each good, no matter what, the income offer curve is the diagonal line through the origin as depicted in Figure G.5A. We have seen that the demand for good 1 is m (pi + p2 so the Engel curve is a straight line with a slope of P + P2 as shown in Figure C.5B.

## Shomu Banerjee Intermediate Microeconomics

The success of the first six editions of Intermediate Microeconomics has pleased me very much. It has confirmed my belief that the market would welcome an analytic approach to microeconomics at the undergraduate level. My aim in writing the first edition was to present a treatment of the methods of microeconomics that would allow students to apply these tools on their own and not just passively absorb the predigested cases described in the text. I have found that the best way to do this is to...

## Cost Minimization

Suppose that we have two factors of production that have prices w and w2 5 and that we want to figure out the cheapest way to produce a given level of output, y. If we let x and x2 measure the amounts used of the two factors and let f x 1,2 2 t gt e the production function for the firm, we can write this problem as The same warnings apply as in the preceding chapter concerning this sort of analysis make sure that you have included all costs of production in the calculation of costs, and make...

## Utility Functions and Probabilities

If the consumer has reasonable preferences about consumption in different circumstances, then we will be able to use a utility function to describe these preferences, just as we have done in other contexts. However, the fact that we are considering choice under uncertainty does add a special structure to the choice problem. In general, how a person values consumption in one state as compared to another will depend on the probability that the state in question will actually occur. In other...

## Demand Revelation

We have seen above that majority voting, even if it leads to a well-defined outcome, will not necessarily provide the correct incentives for people to honestly reveal their true preferences. In general, there will be an incentive to misrepresent preferences in order to manipulate the voting outcome. This observation leads to the issue of what other methods there might be that would ensure that individuals have the proper incentives to correctly reveal their true preferences about a public good....

## Hayden Economics Book

That is, the cost per unit of output will be constant no matter what level of output the firm wants to produce. If the technology exhibits increasing returns to scale, then the costs will increase less than linearly with respect to output, so the average costs will be declining in output as output increases, the average costs of production will tend to fall. Similarly, if the technology exhibits decreasing returns to scale, then average costs will rise as output increases. As we saw earlier, a...

## Qi Piyi xi

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...

## 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...

## 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...

## 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...

## 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

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...

## 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...

## 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...

## 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

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...

## 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...

## Quasilinear preferences An income offer curve A and an Engel curve B with quasilinear preferences

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,...

## 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...