The perfectly competitive equilibrium is known for being an efficient market outcome. But what does it mean for a market outcome to be efficient? Let’s look at a few ways in which competitive equilibrium embodies the concept of efficiency.
First, notice how the transaction in a competitive market are distributed. The far left end of the demand curve captures the individuals with the highest willingness to pay for the good; similarly, the left end of the supply curve captures the sellers with the lowest marginal cost. Therefore, the “first” transactions to occur are transactions between the individuals who value the item the most (in terms of WTP) and the sellers who are most efficient at producing this item (captured by the low marginal cost).
To see why this is efficient, consider an extreme example. If only one unit was going to be exchanged, it would be efficient for that one unit to (1) be produced by the seller who can do it at the lowest cost and (2) be purchased by the buyer who values it most based on her WTP. Why should a higher cost seller be able to sell a unit in a market when a seller who is able to produce the same unit at a lower cost cannot sell? Efficiency ensures sellers with the lowest cost and buyers with the highest value are most able to transact. We can apply this principle to all units in the market: as additional units are exchanged, they should continue to be produced by the next lowest cost seller and sold to the next highest WTP buyer.
Figure5.7.1.The first few transactions which occur are between high WTP consumers and low marginal cost sellers. As more transactions occur approaching \(Q^*\text{,}\) WTP decreases and marginal cost increases.
As a result of this principle, at a perfectly competitive equilibrium, there are two simultaneous consequences:
Every transaction that occurs is a mutually beneficial transaction.
No transaction that does not occur is a mutually beneficial transaction.
A mutually beneficial transaction is a transaction that benefits both the buyer and seller. A transaction is beneficial for a buyer if the buyer pays a price below (or equal to) her willingness to pay; a transaction is beneficial for a seller if the seller receives a price above (or equal to) their marginal cost. Combined, a transaction is mutually beneficial is the buyers pays a price below her WTP to a seller whose price is above their MC. It is efficient for any mutually beneficial transaction to take place: if an exchange makes both parties better off, we should make it happen!
Consider this numerically in the graphical example below. Here, the equilibrium price in the market is \(P^* = 20\text{.}\) Suppose the fifth highest WTP consumer in the market is willing to pay $35 for the unit, and the fifth lowest cost seller can produce the unit for a marginal cost of $10. Since the consumer is getting a price $15 less than her willingness to pay, and the seller receives a price $10 above its marginal cost, this transaction would benefit both parties. For the market to be efficient, this transaction should happen! And of course, at competitive equilibrium, this transaction does happen!
Figure5.7.2.Left: At \(P^* = 20\text{,}\) for the fifth transaction, WTP = 35 and MC = 10. Since both sides of the transaction benefit, it should take place. Right: At \(P^* = 20\text{,}\) for the fifteenth transaction, WTP = 15 and MC = 30. Since neither side of the transaction benefits, it should not take place.
Let’s extend the example to look at a transaction that does not happen. Consider unit number 15, where the market price again is \(P^* = 20\text{.}\) Now the fifteenth highest WTP consumer is willing to pay $15 for the unit, while the fifteenth lowest \(MC\) seller can produce the unit at a cost of $30. Should this transaction take place? It isn’t rational for this consumer to buy the unit, since she would pay $20 for a unit she only values at $15. Likewise, the seller would not find it rational to produce a unit for $30 and only receive $20 for it. This transaction should not take place! Fortunately, since at equilibrium, the quantity exchanged does not reach 15, this guarantees that at equilibrium, no transaction that is not mutually beneficial will take place.
In short, one way to view competitive equilibrium is to recognize that at equilibrium, every transaction that happens is a mutually beneficial one and every transaction that does not happen would not have been mutually beneficial anyway.
Figure5.7.3.All transactions to the left of and included in the equilibrium quantity are mutually beneficial (marked with a \checkmark); all transactions beyond the equilibrium quantity are not mutually beneficial (marked with an \(X\)).
We can tell this story by turning back to the notion of consumer surplus and its analogue for sellers, producer surplus. Recall that consumer surplus measures the benefit a consumer receives from a transaction by calculating the difference between the buyer’s willingness to pay and the price they actually pay. In a similar fashion, producer surplus measures the benefit a seller receives from a transaction by calculating the difference between the seller’s marginal cost of production and the price they receive. So, for example, a firm who receives a price of 20 for a good which has a marginal cost of 10 would receive a producer surplus of \(PS = P - MC = 20 - 10 = 10\text{.}\)
Economists often refer to the lowest price a seller is willing to accept as the seller’s reservation price. The term reservation price is a more direct counterpoint to a buyers’ willingness to pay. If a seller is also the producer of a good or service, then in most cases, the lowest price the seller is willing to accept is the cost of producing the good. It is common to see reservation prices in many selling contexts, such as eBay auctions or craigslist, where a seller lists a price below which they are not willing to sell.
Just as consumer surplus is visualized as the vertical distance between the demand curve and the price, producer surplus can be visualized as the vertical distance between the price and the supply curve. For a single seller, its producer surplus is a vertical strip, while the total amount of producer surplus across all sellers is the total area below the price and above the supply curve.
Figure5.7.4.Left: For a given transaction, the consumer surplus of that unit is the vertical difference between WTP (\(D\)) and the price. Right: For a given transaction, the producer surplus of that unit is the vertical difference between the price and marginal cost (\(S\)).
We can use the concepts of consumer and producer surplus to reframe efficiency at competitive equilibrium. At equilibrium, since the first units go to the lowest cost sellers and highest WTP buyers, the first units exchanged generate the highest consumer and producer surplus. As additional units are sold, CS and PS are still positive. Importantly, any transactions beyond \(Q^*\) do not take place: these transactions would generate negative consumer and producer surplus.
Figure5.7.5.Left: Early transactions generate large consumer surplus and producer surplus. Right: Later transactions generate smaller but still positive consumer surplus and producer surplus.
Let’s call the total surplus (TS) in the market the total amount of benefit that goes to all participants, which here, are all buyers and sellers. Formally, here, we can compute total surplus by summing:
\begin{equation*}
TS = CS + PS
\end{equation*}
This gives us another angle from which to think about efficiency. At competitive equilibrium, the market outcome is efficient because it maximizes total surplus. Equilibrium generates the greatest amount of total benefit to the combined group of buyers and sellers in the market. It does this by allowing all opportunities for mutually beneficial transactions are taken!
Figure5.7.6.Left: Consumer surplus (CS) and producer surplus (PS) areas are the sum of all of the vertical strips representing consumer surplus and producer surplus for each transaction. Right: Total surplus (TS) is the sum of consumer surplus and producer surplus.
If the price were too high or too low, a market adjustment would increase total surplus by allowing additional mutually beneficial transactions to occur. Consider the example from above, where demand is \(Q_D = 300 - 20P\text{,}\) supply is \(Q_S = 30P\text{,}\) and a shortage of 50 units exists at a price of $5. The market outcome is \((P, Q) = (5, 150)\text{,}\) and CS and PS can both be measured. Producer surplus is the triangular area above the supply curve and below the price:
The market outcome \((P, Q) = (5, 150)\) generates $375.00 in benefit to sellers collectively. What about consumer surplus? The area below the demand curve and above the price is now a trapezoid, because consumer surplus only applies to the 150 transactions which occur. How can we find this area? The easiest method is to (1) find the price at which \(Q_D = 150\text{;}\) according to the demand function (setting \(150 = 300 - 20P\)), this price is 7.50. Then, we can (2) compute the area of the trapezoid by combining the area of the triangular section on top and the rectangular area in the middle:
The market outcome \((P, Q) = (5, 150)\) generates $937.50 in benefit to buyers collectively, and the total surplus is $375.00 + $937.50 = $1312.50. But we recognize that there is a shortage at this outcome. The price is too low! (In fact, the low price is why consumer surplus is so much larger than producer surplus.) We know an upward price adjustment will move the market closer to equilibrium. How does an upward movement impact surplus?
If the price adjusts upward to $5.50, the new market outcome (as we have seen) is \((P, Q) = (5.50, 165)\text{.}\) Producer surplus remains triangular:
Producer surplus grows, which makes sense for two reasons! First, 15 more sellers get to sell, so benefits to sellers are spread to more sellers. Plus, every seller who sells now gets to sell for a higher price! These two factors work together to show an unambiguous increase in producer surplus as the market adjusts.
What about consumer surplus? If we try to tell the same story, the two factors here don’t work together the same way. While it is true that 15 more buyers will get to buy at the new market outcome, each buyer must now pay a higher price. So, how does this tradeoff affect consumer surplus after the price adjustment to 5.50? Let’s calculate 1 :
Consumer surplus actually goes down slightly after the adjustment. We can interpret this drop by saying that the price increases (which affects all buyers) outweighs the higher number of buyers participating in the market. But, what about total surplus? Total surplus after the adjustment is
Compared to before the adjustment, total surplus has grown from $1312.50 to $1340.63. The adjustment toward equilibrium increases the efficiency of the market by increasing the total amount of benefits to all participants. Even though this adjustment makes sellers collectively better off and buyers collectively worse off, the boon to sellers outweighs the decrease to buyers.
Figure5.7.7.Left: At a price of 5, consumer surplus (trapezoid) is \(CS = 937.50\text{,}\) while producer surplus (triangle) is \(PS = 375\text{.}\) Right: At a price of 5.50, consumer surplus decreases to \(CS_2 = 886.88\text{,}\) while producer surplus increases to \(PS_2 = 453.75\text{.}\)
If we take this adjustment all the way to equilibrium, we can compute that \(CS^* = \frac{1}{2}(9)(180) = 810\text{,}\)\(PS^* = \frac{1}{2}(6)(180) = 540\text{,}\) and total surplus is \(TS^* = \$1350\text{.}\) Equilibrium maximizes the total surplus in the market!
This section leaves us with two comparable ways to think about the efficiency of equilibrium in competitive markets. At an efficient outcome:
Every opportunity for a mutually beneficial transaction is taken.
Total surplus is maximized.
The efficiency of competitive equilibrium is a useful benchmark for the study of many policy choices. There may be markets where policy makers wish to prioritize the efficiency of markets, while in other markets, a policy decision which sacrifices efficiency to distribute benefits differently is made. This tradeoff between maximizing efficiency (creating the largest pie) and determining how surplus is distributed among buyers and sellers (who gets how big of a slice of the pie) is at the heart of the policy questions we will analyze in the next section.
In Depth5.7.8.Are consumer surplus and producer surplus equal?
Short answer: nooooooooo. Consumer surplus and producer surplus are not necessarily equal! There is no reason for them to be equal. Sometimes economists draw a supply and demand graph that makes them look equal, but this is only out of an odd affection for symmetry. In the graphs and examples above, consumer surplus and producer surplus are very clearly not equal. While they can be equal, there is no inherent reason whatsoever for them to be equal.
