1. Consumers, Producers, and the Efficiency of markets
Econ 100
Lecture 9
Whether the quantity bought and sold in the equilibrium of a perfectly competitive market is too small, too large or just right:
Consumers, Producers, and the Efficiency of markets

2. So far, we have seen how prices and quantities bought and sold of specific goods and services are determined in perfectly competitive markets.
But we have not yet asked the question of what prices and quantities should be. In other words, we have not yet examined whether for example the equilibrium quantity in market is to little, too high, or just right.
In order to be able to address that question, we have to develop some tools and criteria
This is what we will do in this lecture, and we will do it in several steps.

3. First, let us consider a buyer who is thinking of buying one (more) unit of a specific good. His decision making can be described most simply as follows:
Under all the given conditions at a certain moment, he will have in mind a maximum price that he will pay for that unit of the good,
so that, if the actual price of the good that he and the seller can agree on is less than (or equal to) this maximum price, he will buy that unit, otherwise he won't.
This price is called the buyer's maximum willingness to pay for that unit of the good, or his reservation price.

4. In other words, let the reservation price of the buyer be denoted by RP and the actual price of the good by P.
The buyer will
buy the unit if RP > P or if RP = P,
not buy it if RP < P.

5. Suppose RP > P and the buyer decides to buy the unit
Suppose RP > P and the buyer decides to buy the unit. Then he will pay for the good an amount which is RP – P less than RP.
In other words, the buyer was willing to pay a price as high as RP for the good, but he is paying only P. The difference between RP and P is taken as a measure of the benefit derived by the buyer from buying (and using) this unit of the good, and it is called buyer surplus (or, consumer surplus if the good is a consumption good).
Consumer surplus (CS) = RP – P
Notice that, if RP = P, the buyer will buy but CS = 0,

6. Next, consider a producer/seller who is thinking of producing and selling one (more) unit of the good. His decision making can be described most simply as follows:
By producing the unit, he will incur a cost (which includes not only the out-of-pocket production cost due to that unit but also the opportunity cost or forgone profits from another activity which is the best alternative to producing this unit).
This cost will represent what the producer is willing to be paid at the minimum for the production and selling of this unit,

7. so that he will decide to produce and sell this unit if he and the buyer can agree on a price which is more than (or equal to) the cost, otherwise he won't.
In other words, let the cost be denoted by C.
The seller will
sell the unit if P > C or if P = C,
not sell if P < C.

8. Suppose P > C and the seller decides to sell the unit
Suppose P > C and the seller decides to sell the unit. Then he will be paid for the good an amount which is P – C more than C.
In other words, the seller was willing to be paid as low as C for the good, but he is being paid P. The difference between P and C is taken as a measure of the benefit derived by the seller from producing and selling this good, and it is called producer surplus.
Producer surplus (PS) = P – C
Notice that, if P = C, the producer will sell but PS = 0.

9. Combining the decisions by the buyer and the seller (or by the consumer and the producer), we see that they will enter in an exchange (and both benefit) if they agree on a price P such that
RP > P > C
with CS = RP – P and PS = P – C
and the total surplus derived by the consumer and producer together will be
Total surplus = RP – P + P – C = RP – C

10. Second, we will see that the demand curve is actually an arrangement that displays the maximum willingness to pay by (or reservation prices of) different buyers for one more unit of the good in decreasing order, and
the supply curve is an arrangement that displays the costs of producing one more unit of the good for different sellers in increasing order.
Let us start with the fact that we have drawn demand curves as continuous curves
but if the good comes in and is sold in discrete units (such as 1, 2, 3, ..., n, n+1, …) then the demand “curve” is actually a graph with...

11. stepwise portions like a staircase where each step can have a different height but has a width equal to one unit. The continuously drawn demand curve is a good approximation when the good is being produced and sold in large quantities.
The continuous demand curve tells us for example that if P is equal to Pn, the quantity demanded will be n units.
This means that if P = or < Pn, n or more units will be demanded.
Suppose P increases starting from a value less than Pn. As soon as P becomes larger than Pn, quantity demanded falls from n to n – 1.

12. This means that the buyer who is buying the n-th unit decides not to buy it if P exceeds Pn. And this, in turn, means that Pn is the maximum price that the buyer who would buy the n-th unit could pay for the n-th unit.
Therefore, a price along a demand curve is the maximum willingness to pay by the buyer who would be buying the last unit in the quantity demanded corresponding to that price.
Similarly, the continuous supply curve for a good that is produced and sold in discrete units can be thought of as an approximation to the true supply curve...

13. which actually looks like a staircase along which each step has a width equal to one unit and the height of each new step is the difference between the cost of producing the unit before and the cost of producing the unit at that step.
The continuous supply curve tell us for example that if the P is equal to Pm, the quantity supplied will be m units.
This means that if P is = or >, m or more units will be supplied.

14. Suppose P decreases starting from a value larger than Pm
Suppose P decreases starting from a value larger than Pm. As soon as P becomes smaller than Pm, quantity supplied falls from m to m – 1.
This means that the producer who is producing the m-th unit decides not to produce it if P falls below Pm. And this, in turn, means that Pm is the minimum price that the producer who would produce the m-th unit could produce the m-th unit for.
Therefore, a price along a supply curve is the minimum willingness to be paid by the producer who would be producing the last unit in the quantity supplied corresponding to that price.

15. We are still trying to find a criterion to tell if the quantity in a perfectly competitive market is too small or too large and if it can be improved upon or not.
As a third step in our attempt, suppose now that the buyer with the n-th highest reservation price (RPn) buys one unit of the good from the producer with the m-th lowest cost (Cm). The total surplus generated from this exchange will be
Total surplus = RPn – Cm

16. On the diagram displaying the D and S curves for the good, this total surplus will be seen as the difference between
the area under the D curve at n
and
the area under the S curve at m.
Furthermore, if the price paid by the buyer to the seller is P, the total surplus can be split into consumer surplus and producer surplus:
Total surplus = (RPn – P) + (P – Cm)

17. Here,
Consumer surplus = area under the D curve and above P at n
and
Producer surplus = area under P and above the S curve at m

18. Suppose now that the buyers with the first n highest reservation prices decide to buy n units of the good from the producers with the first n lowest costs.
What is the total surplus generated from the exchange of all n units?

19. Sum of total surplus of all units from 1 to n
= sum of (RP – C) for all units from 1 to n
= sum of first n RPs – sum of first n Cs
= area under the D curve from the first to n-th unit
– area above the S curve from the first to n-th unit
Furthermore, suppose that each buyer is paying the same price P to the seller from whom he is buying a unit. What can we say about the consumer surplus and producer surplus generated from the exchange of all these n units?

20. On the diagram we see them as
Consumer surplus = area under the D curve and above P from the first to n-th unit
and
Producer surplus = area under P and above the S curve from the first to n-th unit
Now we are almost ready to assess If the quantity produced and sold in a perfectly competitive market is just right or not.

21. Now imagine that you are a social planner and your objective is to make the total surplus from the exchange of the quantity bought and sold in a perfectly competitive market as large as possible. You have to decide on the following:
What should be the number of units produced and sold and consumed?
Who should produce and sell and who should buy and consume these units?
At what price should each unit be bought and sold?

22. As we try to answer these questions, let us go back to drawing the D and S curves continuously (because we know what they mean).
First of all, in order to maximize the total surplus at any number of units Q, Q should be produced and sold by the producers with the lowest costs and purchased and consumed by the consumers with the highest reservation prices. This means that
total surplus = area under the D curve and above the S curve between 0 and Q units

23. If Q is less than Qe (quantity at the equilibrium of the market), the area which the total surplus is equal to will appear as a trapezoidal area.
Let P1 be the price along the D curve at Q and P2 be the price along the S curve at Q. If all buyers are required to pay the same price, any quantity less than Qe can be realized as long as the price P is set anywhere between P1 and P2.
Consumer surplus will again be equal to the area under the D curve and above P and producer surplus to the area under P and above the S curve, both between 0 and Q units.

24. But even if you choose at any Q the consumers with the highest reservation prices and producers with the lowest costs, there still remains the question of what Q itself should be so that the total surplus is made as large as possible.
By inspecting the diagram, we see that the total surplus can be increased by increasing Q up to Qe.
Notice that for all the units of the good between 0 and Qe, RP > C so that the additional total surplus per additional unit produced and sold is positive, and that's why total surplus increases as Q is increased when it is less than Qe.

25. But Q should not be increased beyond Qe, because for all the units of the good beyond Qe, RP < C so that the additional total surplus per additional unit produced and sold is negative, and total surplus would begin to decrease if Q is increased beyond Qe.
It follows that total surplus is maximized at Q = Qe. Notice also that the price should be set at P = Pe.
These mean that the price and the quantity at the equilibrium of a perfectly competitive market maximize the total surplus derived by buyers and sellers (or, by consumers and producers) who take part in that market.

26. One can ask if equilibrium price and quantity maximize the total surplus also for the society.
Note that RP and C measure the benefits and costs as evaluated by the consumer and producer.
If no party other than the consumer and producer derives any benefits and incurs any costs from the consumption and production of this unit (which is a situation referred to by saying that there are no externalities), then neither any benefits nor any costs are omitted in the calculation of the total surplus
and the total surplus derived by the consumer and producer...

27. coincides with the total surplus derived by the entire society of which the consumer and producer are part of, or we can say that
the total surplus measures not only the surplus derived by the consumer and producer but also by the entire society of which the consumer and producer are part of.

28. Therefore, we can express our findings as follows:
Equilibrium price and quantity in a market for a specific good or service are best in the sense that they maximize the total surplus (or the total net benefit) from the production and consumption of that good or service if
The market for that good or service is perfectly competitive (or, there is no imperfect competition) and
There are no externalities associated with the production and consumption of that good.

29. In such a situation, we talk about
the market being efficient,
or the resource allocation obtained as a result of the market outcome being efficient,
or the quantity produced and sold of the good or service being best or right (that is, neither too small nor too large) etc.
It is important not only to understand that markets do not yield efficient outcomes under the presence of imperfect competition or externalities, but also to understand what efficiency implies if it is there.

30. Note that, in order that the total surplus is maximized, the goods are produced by the producers with the lowest costs and sold to the buyers with the highest reservation prices.
This means that the efficient outcome is obtained at the cost of leaving some buyers and sellers out of the market.
Moreover, the buyers with the highest reservation prices are not necessarily those who have the highest preferences or the strongest need for the good.

31. Since the reservation price or maximum willingness to pay for a good also depends on the income of the buyer, those with the highest reservation prices may also be the richer buyers.
Hence, perfectly competitive markets for goods and services allocate resources in the best way from the point of view of the society but they do it for a given income distribution among the members of the society.