Market Equilibrium and Consumer and Producer Surplus: Study Guide (Microeconomics 2.6)

Putting demand and supply together

In Topics 2.1 and 2.2 you studied buyers and sellers separately. Neither side alone sets a price. Buyers want to pay little; sellers want to receive a lot. A market brings them together, and the price that results depends on both.

The supply and demand model is a tool for explaining what makes prices and quantities what they are. It also explains why prices differ from one market to another (why a diamond costs more than a loaf of bread) and why they change over time (why the price of a crop rises after a poor harvest). This topic looks at the resting point of the model; Topic 2.7 looks at what happens when conditions change.

The model in this topic assumes a perfectly competitive market: many buyers and many sellers of an identical good, none of whom can set the price alone.

Market equilibrium

Market equilibrium is the price and quantity at which the quantity buyers wish to buy equals the quantity sellers wish to sell. At that price:

• every buyer who is willing to pay the price can buy;
• every seller who is willing to sell at the price can sell;
• there is no shortage (buyers left wanting more) and no surplus (sellers left with unsold goods). We say the market clears.

On a graph, equilibrium is where the demand and supply curves cross. In a table, it is the row where quantity demanded equals quantity supplied.

Why the market settles there

Suppose the price is above equilibrium. Sellers offer more than buyers want, so unsold goods pile up. Sellers cut their prices to sell their stock, which raises quantity demanded and lowers quantity supplied until the gap closes.

Suppose instead the price is below equilibrium. Buyers want more than sellers offer, so there is a shortage. Buyers compete for the goods and sellers find they can charge more. The price rises until the gap closes.

Either way, the price moves towards equilibrium. Once there, nobody has a reason to change it. That is why the equilibrium is stable. Topic 2.7 looks at shortages and surpluses in detail.

The price as a signal

In a market economy no one tells farmers how much to grow or factories what to make. The equilibrium price does much of this work. It carries information to everyone who makes decisions:

• To buyers, a high price says “this good is scarce compared with how much people want it”. Buyers who value it less use less, or find substitutes. The price rations the good to those who value it most.
• To sellers, a high price says “people value this good highly”. It gives an incentive to produce more and to move resources (workers, land, machines) into making it.
• A low price sends the opposite messages: use more of this; move resources elsewhere.

So prices help decide what is produced and who gets it. This is how a market answers the basic questions of resource allocation from Topic 1.2.

Consumer surplus

Each buyer has a willingness to pay: the highest price at which they would still buy a unit. This reflects the marginal benefit they get from it. The height of the demand curve at each quantity shows the willingness to pay for that unit.

Most buyers pay less than the most they would have paid. The difference is a gain to them:

Consumer surplus for one unit = willingness to pay − price paid

If you would pay up to $10 for a cup of juice and the price is $5, your consumer surplus on that cup is $5.

Add this up for every unit bought and you get the market’s consumer surplus (CS). On a graph, it is the area below the demand curve and above the price, from zero up to the quantity traded. With a straight-line demand curve it is a triangle.

Producer surplus

Each seller has a minimum acceptable price: the lowest price at which they would still sell a unit. This reflects the marginal cost of producing it. The height of the supply curve at each quantity shows that minimum price.

Most sellers receive more than their minimum. The difference is a gain to them:

Producer surplus for one unit = price received − minimum acceptable price

The market’s producer surplus (PS) is the area above the supply curve and below the price, from zero up to the quantity traded. With a straight-line supply curve it is also a triangle.

Total surplus = consumer surplus + producer surplus. It measures the whole gain from trade in the market: the total benefit to buyers minus the total cost to sellers, for every unit traded. Economists use these surpluses to measure how much a market helps buyers and sellers, and whether it is efficient.

Why equilibrium maximises total surplus

Think about one more unit at a time. A unit adds to total surplus when its marginal benefit (the height of demand) is greater than its marginal cost (the height of supply).

• Left of equilibrium, demand lies above supply. Every unit there is worth more to some buyer than it costs some seller to make, so trading it adds to total surplus.
• At equilibrium, marginal benefit equals marginal cost. The last unit traded is just worth making.
• Right of equilibrium, supply lies above demand. Each extra unit would cost more to make than it is worth to any remaining buyer, so producing it would reduce total surplus.

In Saltmere, at 500 cups the 500th cup is worth $7 to a buyer and costs $4 to make: there is $3 of surplus still to gain. At 900 cups the 900th cup is worth only $3 but costs $6 to make. Only at 700 cups, where both are $5, is there no gain left and no loss.

So a perfectly competitive market, with no market failures, trades exactly the quantity that makes total surplus as large as possible. That is what economists mean when they say such a market is efficient. Unit 6 shows cases where this breaks down, such as pollution, when the supply curve does not reflect every cost.

Worked example 1: equilibrium and surplus from a table

Question. Saltmere is a fictional coastal town. The daily market for fresh mango juice is:

Price ($ per cup)	2	3	4	5	6	7	8
Quantity demanded (cups per day)	1,000	900	800	700	600	500	400
Quantity supplied (cups per day)	100	300	500	700	900	1,100	1,300

The demand curve is a straight line that reaches the price axis at $12. The supply curve is a straight line that reaches the price axis at $1.50.

(a) Find the equilibrium price and quantity. (b) Calculate consumer surplus, producer surplus and total surplus at equilibrium. (c) What is buyers’ total spending at equilibrium, and why is it not the same as consumer surplus?

(a) Look for the row where quantity demanded equals quantity supplied. At $5, both are 700. Equilibrium price = $5 per cup; equilibrium quantity = 700 cups per day.

Check the rows either side. At $4 buyers want 800 but sellers offer 500: a shortage of 300, so the price would rise. At $6 sellers offer 900 but buyers want 600: a surplus of 300, so the price would fall.

(b) Use Figure 1.

1. CS is the triangle with base 700 cups and height from $5 up to $12, which is $7. CS = ½ × 700 × 7 = $2,450 per day.
2. PS is the triangle with base 700 cups and height from $1.50 up to $5, which is $3.50. PS = ½ × 700 × 3.50 = $1,225 per day.
3. Total surplus = 2,450 + 1,225 = $3,675 per day.

(c) Spending = price × quantity = 5 × 700 = $3,500 per day. This is the rectangle below the price line, and it is a transfer from buyers to sellers. Consumer surplus is the area above the price line: the benefit buyers get on top of what they pay.

Check. Units: a base in cups times a height in dollars per cup gives dollars. CS is larger than PS here because the demand curve is further above the price than the supply curve is below it.

Worked example 2: surplus with individual buyers and sellers

Question. At a fictional Saturday market in Brindle, five people want to buy a used bicycle and five people have one to sell. Each buyer wants one bicycle; each seller has one.

	1st	2nd	3rd	4th	5th
Buyers’ willingness to pay ($)	95	80	65	50	40
Sellers’ minimum acceptable price ($)	30	45	55	70	85

(a) Find the equilibrium quantity and the range of equilibrium prices. (b) The price settles at $60. Calculate consumer, producer and total surplus. (c) Show that trading a fourth bicycle would lower total surplus.

(a) Pair the keenest buyer with the cheapest seller, and so on. Trade is worth it while willingness to pay is at least the seller’s minimum:

• 1st pair: 95 ≥ 30 ✓; 2nd: 80 ≥ 45 ✓; 3rd: 65 ≥ 55 ✓; 4th: 50 < 70 ✗.

So 3 bicycles are traded. At any price from $55 to $65, three buyers want to buy and three sellers want to sell. (At $52, only two sellers would sell: a shortage. At $68, only two buyers would buy: a surplus.)

(b) At $60:

1. CS = (95 − 60) + (80 − 60) + (65 − 60) = 35 + 20 + 5 = $60.
2. PS = (60 − 30) + (60 − 45) + (60 − 55) = 30 + 15 + 5 = $50.
3. Total surplus = 60 + 50 = $110.

Check. Total surplus is also the sum of (willingness to pay − minimum price) for each pair traded: (95 − 30) + (80 − 45) + (65 − 55) = 65 + 35 + 10 = $110. If the price were $56 instead, CS would be $72 and PS $38: the same $110, split differently.

(c) The 4th buyer values a bicycle at $50, but the 4th seller needs at least $70. Forcing that trade adds 50 − 70 = −$20, so total surplus would fall to $90. Stopping at two bicycles would lose the 3rd pair’s $10, leaving $100. Total surplus is largest, at $110, at the equilibrium quantity.

Interpretation. The market sorts itself. The buyers who value bicycles most get them, and the sellers who part with them most cheaply sell. No planner needed this information; the price did the matching.

Common misconceptions

• “At equilibrium, consumer surplus equals producer surplus.” Not in general. Their sizes depend on the shapes of the two curves. In Worked example 1, CS is twice PS.
• “Consumer surplus is the total amount buyers spend.” Spending is price × quantity. CS is the area above the price and below demand.
• “Producer surplus is the same as profit.” Producer surplus is price minus the minimum acceptable price on each unit. It is not the same measure as profit, which Unit 3 covers.
• “Equilibrium means demand equals supply.” Precisely, it means quantity demanded equals quantity supplied at one price. Demand and supply are whole curves.
• “A lower price is always better for society, because consumer surplus rises.” A price held below equilibrium cuts the quantity traded and lowers total surplus (Topic 2.8).
• “Total surplus depends on the price.” It depends on the quantity traded. The price only splits it between buyers and sellers.
• “I can forget the ½.” A straight-line surplus area is a triangle: ½ × base × height.

Where this leads

Next, Topic 2.7 shows what happens in market disequilibrium and when equilibrium changes, using shifts like those in Topic 2.5. Topic 2.8 then shows how government interventions such as price controls and taxes change consumer and producer surplus and create deadweight loss. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate. For how demand responds to income and related prices, look back at other elasticities.