Question

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: A: $3 B: $6 C: $4 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?

Answer 1

To determine the efficient allocation of haircuts, we need to match consumers willing to pay the highest prices with businesses that have the lowest costs.

1. Ordering consumers and businesses:

- Ordering the consumers by their willingness to pay: Claire ($8), Gloria ($7), Phil ($5), Jay ($2)

- Ordering the businesses by their costs: D ($2), A ($3), C ($4), B ($6)

2. Efficient allocation:

- Since there are four consumers and four businesses, each consumer will receive one haircut.

- Assign the haircuts in descending order of willingness to pay and ascending order of costs:

- Claire ($8) should have her hair cut by business D ($2)

- Gloria ($7) should have her hair cut by business A ($3)

- Phil ($5) should have his hair cut by business C ($4)

- Jay ($2) should have his hair cut by business B ($6)

3. Maximum possible total surplus:

- Total surplus is the sum of the differences between the willingness to pay and the cost for each haircut.

- Total surplus = (Claire's willingness to pay - cost of business D) + (Gloria's willingness to pay - cost of business A) + (Phil's willingness to pay - cost of business C) + (Jay's willingness to pay - cost of business B)

- Total surplus = ($8 - $2) + ($7 - $3) + ($5 - $4) + ($2 - $6)

- Total surplus = $6 + $4 + $1 + (-$4)

- Total surplus = $7

Therefore, the efficient allocation of haircuts is one haircut per consumer, with businesses D, A, C, and B serving Claire, Gloria, Phil, and Jay, respectively. The maximum possible total surplus is $7.

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