Surplus Revisited

Wednesday, October 17, 2001

It has come to the attention of the TAs that some people are having difficulty with the deadweight loss problems and understanding what's going on with surplus when we impose some kind of policy.

Really, all we've given you guys is a special case or two and said that "Okay, now you know how to do it." I know it isn't really clear that something is true in all cases just because we've shown you one situation where it worked. What I will do on this page is run through how I think about surplus for myself and then on a different page go through a laundry list of every damn policy change I can think of. Hopefully this will convince you that the notion of distortion leading to deadweight loss is a general one, and that it's this change in behavior that's really screwing things up.

Consumer Surplus: Do not taunt Happy Fun Ball

First let's look at consumers. Why does a consumer buy a product? We like to have things because they make us happy. We can imagine people putting a "happiness valuation" on money - you are only willing to buy something if it makes you happy enough to justify spending the money price on it. If you've ever thought "That's pretty good, but it isn't $20 good," then that's exactly the idea we're after when we say Willingness To Pay.

Obviously, the people who get the most happiness out of a good will be willing to pay the most for it. That pie will make me so happy that I am willing to pay a lot for it. How much am I willing to pay for it? I am willing to pay the money equivalent of all the happiness I would get out of consuming the pie. So if a pie is worth $7 to me, i'd be willing to pay just about $7 to get it. I'd be no worse off even if the price of the pie was $7, so I am still going to buy it.

The way I always think of markets is that each consumer only wants to buy one unit of the good at most - so they either buy 1 or 0. What we can do is line up all the potential buyers from highest to lowest willingness to pay (this is the same thing as lining them up according to who gets the most happiness out of consuming the good) as follows:

Since we figure that we want the highest happiness valuation guy to get the good first, we line them up from highest to lowest.

Now if we put a line that traces out their valuations, we get a demand curve. How so? Because I assumed each guy wants to buy either one or zero, the height of the demand curve at each bar is the maximum price you could charge and still get that bar's guy to buy. So if you look at the height of the demand curve at the 5th bar, you get the price where exactly the first five guys would buy (you buy if the price is less than or equal to your valuation).

Okay, we have constructed a demand curve. So how do we figure out what consumer surplus is? The way I think of consumer surplus is that Consumer Surplus is any happiness the demanders didn't have to pay for. Let's take our demand curve and put a price in there:

As always, if you give me a price, I can tell you exactly how many units are demanded by looking at the demand curve. Let the equilibrium Price Paid By Consumers in this market be P* for some reason. Then we know that Q* is demanded. The 64 dollar question is now what consumer surplus is.

What are these consumers actually paying? Total Expenditures equals Price Paid by Consumers times Quantity. Everything in the orange is being paid by consumers to acquire the good. Since these 6 guys bought the good, we know that they must have at least gotten back P* worth of happiness each. What's the remaining green stuff above the orange expenditures? Well, the first five guys got more happiness back than they paid - this is pure bonus to them. Consumer Surplus is any happiness the demanders didn't have to pay for. The remaining green stuff above the orange expenditures is the consumer surplus in this market. That 6th guy didn't make out so good. He paid in P* and got back P* happiness. So it's a wash for him - he ends up just about as well of as he was before. *shurg*

Producer Surplus: Big Money, Big Prizes

Now we need to think about producers. Why do firms make and sell products? Firms want to turn a profit. A firm spends some money to make a product and then sells each unit at the market price. Suppose we consider producers like in the Talk Show Host Haircut problem from problem set 2. Each producer can produce either 0 or 1 unit for some cost.

A firm will calculate its Profit, which is equal to Revenue minus Costs. If a producer decides to make a unit and sell it, he incurs his own cost of production and gets back the market Price Received By Producers. Since firms want to make profit, will they ever decide to produce when their cost exceeds the revenues they will get back? Of course not; negative profit is a loss for these guys and nobody wants to take a loss. Firms will decide to produce anytime the revenue they get back is at least enough to cover the cost of making the good.

Since we figure that we want the lowest cost producers to start making the good first, we line them up from lowest to highest cost.

Now if we put a line that traces out their costs, we get a supply curve. How so? Because I assumed each guy wants to make either one or zero, the height of the supply curve at each bar is the minimum price firms need to receive to get that last guy to decide to make a good and sell it. So if you look at the height of the supply curve at the 5th bar, you get the price where exactly the first five guys would sell (you sell if the price received is more than or equal to your cost of production because that means nonnegative profits).

Now let's put a price on this market and use our supply curve to figure out which guys decide to make and sell a unit. The Producer Surplus is equal to any Revenue that isn't used to cover costs. Producer surplus is bonus money the firm got above and beyond what it cost them to make the stuff they sold.

If you give me a price, I can tell you how many units are going to be supplied. Any producer with cost less than or equal to the price will decide to in fact make and sell a unit. Let the equilibrium Price Received By Producers in this market be P* for some reason. Then we know that Q* is supplied. The 64 dollar question is now what producer surplus is.

How much revenue did the firms make? Total Revenue equals Price Received By Producers times Quantity. The red part of the diagram shows what it cost these firms to make the goods that got sold. The blue part of the diagram is the portion of revenue that was above and beyond what it cost them to make the goods. Producer surplus is bonus money the firm got above and beyond what it cost them to make the stuff they sold. Therefore, the blue part is Producer Surplus in this market. What about that ninth firm all the way on the right? They didn't make out that well in this market. They got exactly enough revenue back to cover their costs of production and didn't make any economic profits.

When you think about what we just did and you look at the next diagram, you should be able to easily see why the green part is consumer surplus and why the blue part is producer surplus:

Consumer Surplus + Producer Surplus + Government Revenue (Zero in this case) = Total Surplus