Question

Look at Tables 4.1 and 4.2 together. What is the total surplus if Bob buys a unit from Carlos? If Barb buys a unit from Courtney? If Bob buys a unit from Chad? If you match up pairs of buyers and sellers so as to maximize the total surplus of all transactions, what is the largest total surplus that can be achieved?

Person	Maximum willingness to pay (\()	Actual price (\))	Consumer surplus (\()
Bob	13	8	5 (=13-8)
Barb	12	8	4 (=12-8)
Bill	11	8	3 (=11-8)
Bart	10	8	2(=10-8)
Brent	9	8	1 (=9-8)
Betty	8	8	0(=8-8)

Person	Minimum acceptable price (\))	Actual price (\()	Consumer surplus (\))
Carlos	3	8	5 (=8-3)
Courtney	4	8	4 (=8-4)
Chuck	5	8	3 (=8-5)
Cindy	6	8	2 (=8-6)
Craig	7	8	1 (=8-7)
Chad	8	8	0 (=8-8)

Short answer

When Bob buys from Carlos, the total surplus is $10.

When Barb buys from Courtney, the total surplus is $8.

When Bob buys from Chad, the total surplus is $5.

The largest possible total surplus for all transactions is $30.

Step-by-step solution

Step 1. Meaning of total surplus

The total surplus is the gain received by both consumers and producers by participating in market exchange. Producer’s gain is measured by producer surplus (equilibrium price-cost of producing), and consumer’s gain is measured by consumer surplus (willingness to pay-equilibrium price).

For example, if Eric is willing to pay $10 for a basket that costs $5 to produce and whose market price is $8, then the consumer surplus is $2 (=10-8), and producer surplus is $3 (=8-5). Thus, the total surplus is $5 (=2+3).

Step 2. Calculating the total surplus for each case

The two tables given below show the consumer and producer surplus:

Person	Maximum willingness to pay ($)	Actual price ($)	Consumer surplus ($)
Bob	13	8	5 (=13-8)
Barb	12	8	4 (=12-8)
Bill	11	8	3 (=11-8)
Bart	10	8	2(=10-8)
Brent	9	8	1(=9-8)
Betty	8	8	0(=8-8)
Total			15 (=5+4+3+2+1+0)

Person	Minimum acceptable price ($)	Actual price ($)	Consumer surplus ($)
Carlos	3	8	5 (=8-3)
Courtney	4	8	4 (=8-4)
Chuck	5	8	3 (=8-5)
Cindy	6	8	2 (=8-6)
Craig	7	8	1 (=8-7)
Chad	8	8	0 (=8-8)
Total			15 (=5+4+3+2+1+0)

Consider the following cases:

• If Bob decides to buy a unit of a good from Carlos, the consumer surplus and producer surplus for this transaction will be $5 each, and hence, the total surplus would be $10 (=CS+PS).
• If Barb decides to buy a unit of good from Courtney, the consumer surplus and producer surplus for this transaction will be $4 each, and hence, the total surplus would be $8 (=CS+PS).
• If Bob decides to buy a unit of good from Chad, the consumer surplus will be $5, and the producer surplus will be $0 for this transaction, and hence, the total surplus would be $5 (=CS+PS).

Step 3. Maximizing the total surplus for all transactions

Suppose you match all the sellers with all the buyers (considering that each seller will produce one unit and each buyer will consume one unit). The following pairs will form so that the total surplus is maximized for each transaction:

Pairs of buyers and sellers	Total surplus (CS+PS)
Bob-Carlos	$10 (=5+5)
Barb-Courtney	$8 (=4+4)
Bill-Chuck	$6 (=3+3)
Bart-Cindy	$4 (=2+2)
Brent-Craig	$2 (=1+1)
Betty-Chad	$0 (=0+0)
Total	$30 (=10+8+6+4+2+0)

The maximum surplus possible is $30, calculated by adding the total surplus for each pair.

Note: A first look at the data would suggest that every buyer should buy from Carlos (who has a maximum producer surplus of $5), or every seller should sell to Bob (who has maximum consumer surplus) to maximize total transactions surplus. This is not true and cannot be determined as the willingness to pay and the minimum acceptable prices change with every output unit.

For example, Bob may not have the same benefits by buying another unit from any other seller. The data shows a unit purchase, and thus, every seller should have a different buyer, and every buyer should have a different seller.