How do social choices get made? Last time we discussed one social choice mechanism, the Pareto Criterion or unanimity rule. This seems like a pretty tough standard to meet. However, it turns out to be the most used method of deciding how society's resources get used in a market economy. Given that the private market allocates the vast majority of the resources in our economy, it's nice to know that (under certain fairly reasonable assumptions) it does so in a Pareto efficient manner.

In a "first best" market with perfect competition and no externalities, anything that can be made which is valued at least as much than the cost of making it gets made. (With perfect competition firms are neither happy nor sad to gain or lose me as a customer.) This is a nice Pareto efficient situation for society. Everything that happens makes everyone involved no worse off and often better off. There is no incentive for people to lie and say that they value some good less than they actually do. The Fundamental Theorem of Welfare Economics or "first welfare theorem" describes how simple market exchange makes everyone at least as well off as before the exchange.

Any competitive equilibrium (CE) is Pareto Optimal (PO) under certain conditions (purely private goods, no externalities).

Let's think about basic microeconomics for a bit here. Recall the model of supply and demand resulting from the interaction of firms, who comprise the supply curve, and consumers, who make up the demand curve. For simplicity, we will assume that there is no fixed factor that drives up firm costs as demand rises, so the supply curve in this example is flat. Also, we will assume the demand curve is of the Hicksian form. Supply and demand curves where formalized by the British economist Alfred Marshall. Marshall's demand curves sloped downward from left to right for two reasons:

1) at a lower price for some good, consumer income would be greater in real terms and thus be able to buy more goods (the income effect),

2) at a lower price, the price of the good would be lower relative to the price of other goods so the consumer would be willing to increase consumption of the good until the marginal utility of consumption fell to the new lower price (the substitution effect).

Hicks modeled the demand curve as assuming that income affects did not matter or were compensated away. (If the price of something you like to buy goes up, so will your income by just enough to allow you the same consumption bundle you originally bought, although you may not choose to buy nearly as much of the new, higher priced, good. The same works for price decreases as well. "What, the price of textbooks went up $20! Hey, look on the floor, it's a twenty! Anyway, I'm gonna drop econ, let's go to Burrito Bay.") Thus, Hicks' demand curves only sloped downward for only the second reason. It's not that Hicks (who came after Marshall) is a dope or something, it's just that for his analysis, he wanted to separate out the income and substitution that are usually mingled in the standard Marshallian demand curve. Anyway, consider Figure 1 where a Hicksian demand and supply diagram (or a Marshallian one where the income effects are really small) and note that in this wonderful case, that

So the price that buyers pay and that sellers receive equates the marginal benefit to society (here the marginal utility of consumption to the buyer) to the marginal social cost (here the marginal cost to the seller). This implies economic efficiency, on the margin we are producing output to the point where we can produce any more for a cost less than or equal to our valuation of the output. That price equals the average cost of production is important because this allows the business to survive. If price were less than AC, then the business would eventually have to fail.

Alternatively, consider the production possibilities frontier (PPF) model of production of two goods combined with consumer indifference curves (Rosen p. 38-47). The stock of society's resources must be divided between the production of two goods and at every efficient point, to get more of one good means giving up some of the other. For goods A and B, this tradeoff is known as the marginal rate of transformation or

MRT_A,B = (df_A(resources)/dresources)/(df_B(resources)/dresources).

[Note: the symbol d denotes "partial differential."]

It's also called opportunity cost by the less nerdishly inclined. The slope of the indifference curve is the ratios of the marginal utilities of the two goods at each point and this is known as the marginal rate of substitution,

MRS_A,B = dU(A)/ dU(B) = MU(A)/MU(B) where MU stands for marginal utility.

At the point of maximum utility, where the indifference curve is tangent to the PPF,

P_A/P_B = dU(A)/ dU(B) = (df_A(resources)/ dresources)/( df_B(resources)/ dresources).

Again, goods are produced to the point where no more can be produced unless the cost of production (here in terms of other goods forgone) is greater than the utility of the extra goods that would be produced.

Chapter 4 in the text goes through a similar line of reasoning in the context of a pure exchange economy using the model of the Edgeworth Box (with Adam and Eve). And again, we get the "first best" result that each person exchanges goods to get to the point were marginal utility over price is equated for each good, we get to an optimal point were for each good no more can be had except at a cost greater than the utility gained from a bit more of the good.

However, we live in a world where much is not "first best." To try to change the amount of public goods or externalities, we may need government action which requires financing in the form of taxes. Taxes will generally screw up the beautiful, simple picture of the world. Now instead of production and consumption being at the point q where

MU(q) = P(q) = MC(q) = AC(q),

we get a different point. Let there be a per unit tax on the producer. This will increase firms' costs of production which will shift the supply curve to the left and the new equilibrium will fall at a point q' which is less than q and where

MU(q') = P(q') = MC(q') + Tax.

Since MU(q') > MC(q'), society could produce a unit of output which would be valued more than the cost of producing it but this does not happen because of the tax. Tragic.

Ah, but how much of private market activity satisfies the assumptions of perfect competition anyway? For monopolists, price is not set at marginal cost and minimum average cost. Monopolists set price (and thus marginal utility for consumers) at the point where their marginal revenue is equal to their marginal cost. Oligopolies follow similar, though more complicated rules. In these cases where P>MC, society could turn some resources into some product of greater value (to consumers) but society chooses not to because doing so would reduce profit to some groups.

Recall that monopolists would be willing to increase production to the point where P=MC, but only if they were able to price discriminate and charge consumers with high marginal utilities of consumption high prices and consumers with low marginal utilities of consumption lower prices, much as airlines do. This gives us the interesting result that price discrimination is economically efficient in that it can set MU = P = MC. So price discrimination can be Pareto improving.

Just as monopoly and oligopoly pricing behavior can keep society from achieving certain Pareto improvements, so can the presence of public goods and externalities. Coming up is a silly example involving Bill and Hillary and their problem about buying a shredder. It had a cost of 4 utils and would benefit each of them 3 utils. If they split the cost equally, they could each gain 1 util. If Hillary bought it on her own, she would lose 4 utils but only gain 3 utils for a net loss of one util. The same goes for Bill. So if they cannot cooperate, then society (Hillary and Bill) loses out on a chance for a net gain of 2 utils. Clearly this "no cooperation" economic equilibrium is not Pareto Efficient, just as monopoly pricing is not. Pareto Efficiency implies that no Pareto Improvements are possible and that would not be the case here.

A common solution to this sort of problem is to have government provision. Publicly provided goods (and services, naturally) could fall into three basic groupings.

1) Public goods - defense, dams, laws

2) Bundled private goods - Natural parks, schools

3) Some quantities of both - roads, city services

The possibility of improving social welfare through government action is the subject of the Second Welfare Theorem. It considers how the situation faced by Bill and Hillary could Pareto Improved through some redistribution.

Second Welfare Theorem

Any PO allocation can be supported as a competitive equilibrium given suitable redistribution of resources.

But here's the rub. How do we make these choices of what to make and how to finance it? It's so simple for private goods, they're basically self financing on a voluntary basis. People who want the goods will identify themselves and offer to pay enough to cover the cost in exchange for the good. It's not easy at all for decisions requiring collective action.

Choice Methods

Clearly society is better off as its members are better off. A Pareto Improvement is inarguably a good thing to do but it's pretty restrictive. Here are some other methods.

One simple approach is that government should do what makes society better off (the mechanistic rational for the existence of government). But who's to say if society is better off? Wouldn't it be great if there were some social welfare function we could maximize? Society faces choices over what it can produce and it would be good to have some function which would rank these choices (like college football teams are ranked). Something like the following where W is social welfare, U_i is the utility of person i, and n is the number of individuals in society.

W = F(U₁, U₂, U₃, ..., U_n)

Jeremy Bentham, John Stuart Mill and the 19th century Utilitarians thought that a simple sum of people's happiness would be a good method. This was before the idea of decreasing marginal utility had been thought about much.

W = U₁ + U₂ + U₃ + U₄ + ... + U_n.

Some obvious questions come to mind about this approach. How would we know what someone's utility really was? How do we compare utility across people? Who do we include in the n members of society?

This last one is quite a problem under most systems, even market systems. Do we count the wishes of people who are dead? Or do we despoil graves and use foundation monies in ways that the now departed founders would find disgraceful? What about the preferences of the unborn? Missouri tried to get these alleged preferences written into the preamble of its state constitution in the form of a statement that a human fetus was a human being. This ran counter to the existing statutes on how many deductions a person could take on income taxes, how to enumerate the population for voting districts and census collection, who could be served alcohol, and exactly how many people were in a vehicle for car-pool lanes on the highway. Should the young be counted equally with the adult? Should the preferences of the young be entrusted to their parents so parents' feelings should be counted more than those of people without children? Do illegal immigrants count? Old people or those soon to die? Felons? Should white male landowners count more? Should slaves count for only three-fifths? Should people in other jurisdictions get some voice, like should South Pacific islanders have some say in how France conducts its nuclear tests?

Should future generations be counted? If so, how? Economist Frank Ramsey believed it was immoral to count their preferences any less than our own and so he opposed social discounting. Are the interests of future generations well cared for by a market system? Will our great-grandchildren weep because they can't see a snail darter? Or because the sun's brightness is diminished by the great circling flocks of spotted owls? Seriously, how will future generations feel about the amount of natural resources we will leave them? James Watt, Reagan's first Secretary of the Interior, stated that this was a foolish concern because the second coming of Christ was imminent and God would be curious about why we did not fully use the bounty we had been given. I don't know if anyone asked Watt how we would be doing now if Teddy Roosevelt or George Washington had shared his view.

If problems with the social welfare function of who counts and how much are solved, what changes would be good to undertake? Nicholas Kaldor and Sir John Hicks (the originator of the ISLM model) came up with a basic approach. They believed that society should undertake any change where the gains to winners were bigger than the losses to losers.

Welfare is improved by any new allocation whereby those who are worse off could be compensated by those who are better off.

Note however, that "could" does not mean "will." NAFTA is a classic example of this. The gains to society as a whole (society here could be defined as any of the three nations directly involved or all of them together) are expected to be small but positive. However, the losses to certain groups may well be huge. The gains to society will almost certainly be larger than the losses to these groups, but these harmed groups are unlikely to be fully compensated. A hypothetical example would be us giving all our wealth to Donald Trump who could use his financial acumen (or his father's) to double its value which he would then keep. This would make us worse off but because Trump could (but won't) compensate us, by Hicks-Kaldor (H-K) scoring, this would be a gain to society. Clearly the H-K Criterion is less restrictive than the Pareto Criterion.

OK, so Pareto schemes are very restrictive and social welfare functions are wickedly subjective. What are some other approaches?

Harvard philosopher John Rawls suggests that society should try to maximize the welfare of the worst-off person, what is known as a "maximin" strategy. He suggests that this is what would be chosen as a "fair" strategy by a group of people who had to choose some social choice mechanism before they had any idea what their positions in life would be. This maximin strategy recognizes that a system which made everyone equally well off would have strong disincentive effects on work effort. So everyone would be equally well off and poor. Under a Rawls type social welfare function, people may be rich or poor but no one would be "too badly off." Rawls basically uses a social welfare function of the following form where U_I is the utility of the "I-th" person, W = min(U₁, U₂, U₃, U₄, U₅, ….).

If society had a choice of giving $1 to someone who had an income of $10,000 or $1.05 to someone with an income of $20,000, which should it do? John Stuart Mill would say that it would depend on the marginal utilities of the two individuals. Rawls would say give the $1 to the person with $10,000. What if society's choice was between giving $1 to someone who had an income of $10,000 or $1,000,000 to someone with an income of $20,000? John Stuart Mill would say that it would depend on the marginal utilities of the two individuals. Rawls would say give the $1 to the person with $10,000.

There's another nice example of a way of purchasing public goods that would fit under the unanimity rule or the Pareto Criterion for social change. Erik Lindahl suggested that a social project was worth undertaking if the cost of the project is less than how much people value it or what they could be charged in terms of their Lindahl prices.

Total Value of Project to Society > Project Cost

Lindahl Price to Person i = (Benefit to person i/Total social benefit) * Cost of Project

Any project undertaken under this strategy would be a Pareto Improvement. No one would have to pay more than the project was worth to him or her so no one would be made worse off. Each person would potentially be paying a price unique to her. Do note that Lindahl prices can be negative for some people.

Here comes that example with Bill and Hillary and the shredder. Let's change it a little to make it more complicated, because examples are only really fun when they're complicated.

Still neither of them would be willing to buy the shredder on his or her own, but society (in the form of Bill and Hillary) could be better off if a shredder could be obtained, even if they had to pay for it somehow.

Notice that the total cost of the shredder to society (here Bill and Hillary) is 9/4 + 15/4 = 24/4 = 6. That is, the sum of what each pays equals the cost of the good.

What is wrong with this approach? Who is going to reveal his or her true feelings about the value of some project if that means a directly higher tax bill? Here's the example of Bill and Hillary and the shredder that I warned you about. Recall that the shredder costs 4 utils and has a value to Bill of 3 utils. If Bill is known for always telling the complete truth and has already reported that the shredder is worth 3 utils to him, Hillary knows that what she say about her valuation of the shredder will determine how much she will have to pay and how much her utility will be. Consider the following possibilities.

• If Hillary says the shredder is worth zero utils to her, it won't be built because its cost is 6 utils and Bill is only willing to pay 3 utils. Neither Bill nor Hillary gain or lose any utility.
• If Hillary says the shredder is worth 3 utils to her, it will get built.
• Total (Reported) Social Value = 3 utils + 3 util = 6 utils = Cost of project
• Lindahl Price_Bill = Share of Benefits * Cost = 3 utils/6 utils * 6 utils = 3 utils
• Lindahl Price_Hillary = 3 utils/6 utils * 6 utils = 3 utils
• Gain to Bill = 3 utils - 3 utils = 0 utils
• Gain to Hillary = 5 utils - 3 util = 2 utils
• If Hillary says the shredder is worth 5 utils to her, it will get built.
• Total (Reported) Social Value = 3 utils + 5 utils = 8 utils > Cost of project
• Lindahl Price_Bill = Share of Benefits * Cost = 3 utils/8 utils * 6 utils = 9/4th utils
• Lindahl Price_Hillary = 5 utils/8 utils * 6 utils = 15/4th utils
• Gain to Bill = 3 utils - 9/4th utils = 3/4th utils
• Gain to Hillary = 5 utils - 15/4th utils = 5/4th utils

So there is a strong incentive for Hillary to under-report her enjoyment of the shredder. Fortunately for Bill, Hillary is unlikely to do this. This incentive to under-report utility would still be there even if the enjoyment to each of them from the shredder would be 5 utils. In this case, each would be willing to buy the good on his or her own but by under-reporting utility, each could reduce the Lindahl price demanded. This is called "rent-seeking" which refers to attempting to change the payment required or received for doing the same thing as at a different payment. This sounds confusing but it's not. It goes back to the work of David Ricardo and will be discussed in some detail later in the class. In this example, with a utility benefit of 5 utils and a cost of 4 utils, either Bill or Hillary would be willing to buy the shredder. However, each would prefer to pay less. An example that might be more in your frame of reference, if you intend to go to Northwestern next quarter, even at full tuition, you still have an incentive to try to get Northwestern to try to give you some financial aid.

[Ah, so what about the "negative utility" example that blew up in my face in class? Here's the deal, if Chelsea got utility of -1 util from this.

Notice that the total cost of the shredder to society (here Bill, Hillary, and Chelsea) is

3 + 5 + (-1) = 7 = the total social cost of the good. So it works, see!

However, I'm cheating here bigtime. If Chelsea has negative utility anything but -1, this doesn't work. So what's going on? The trick is that this works if we are equating things on the margin, that is where the marginal social benefit is equal to the marginal social cost. This example where the cost of production was 6 utils, take it or leave it, makes things a bit messy. This will become clearer when we do chapter five where we will derive the optimal level of the public good (which will be soon, not just pick some level at random. Unlike optimal choice of private goods where all the consumers pay the same price but buys whatever quantity suits them best, with a Lindahl priced public good, each consumer must face a different price that induces him or her to want to consume the same amount of the public good as everyone else. This will make more sense soon, really.]

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Questions, typos, comments? mwitte@nwu.edu