There are four consumers willing to pay the following amounts for haircuts:

Gloria: $7

Jay: $2

Claire: $8

Phil: $5

There are four haircutting businesses with the following costs:

Firm A: $3

Firm B: $6

Firm C: $4

Firm D: $2

Each firm has the capacity to produce only one haircut.

For efficiency, how many haircuts should be given? Which businesses should cut hair and which consumers should have their hair cut? How large is the maximum possible total surplus?

3 haircuts to be provided

Firm A should cut the hair of Claire

Firm C should cut the hair of Gloria

Firm D should cut the hair of Phil

Explanation:

The surplus of the

a. 1st haircut is $8 (its advantage, which equals C's willingness to pay for) subtract $2 (the cost of firm D to offer it).

b. 2nd haircut is $7 (its advantage, which equals G's willingness to pay for) subtract $3 (the cost of firm A to offer it).

c. 3rd haircut is $5 (its advantage, which equals P's willingness to pay for) subtract $4 (the cost of firm C to offer it).

d. 4th haircut is $2 (its advantage, which equals J's willingness to pay for) subtract $6 (the cost of firm B to offer it).

It could be observed that the surplus from each of the first three units is positive (that is $6, $4 and $1). The surplus of the 4th one is negative (-$4).

Therefore, in order to maximise the aggregate surplus, 3 haircuts should be given.

Firm A should cut the hair of Claire

Firm C should cut the hair of Gloria

Firm D should cut the hair of Phil

And Firm B will not participate as its cost is too high as compare to other firms.

Maximum aggregate surplus = $6 + $4 = $1

= $11

Note that the aggregate demand is equal to aggregate supply at the quantity of 3 haircuts and the price between $4 and $5. So, it could be a precise prediction for the equilibrium quantity which is 3 but any price among $4 and $5 could the equilibrium price. Therefore, the equilibrium quantity maximises the aggregate surplus.