Table 18-1
Imagine a small town in which only two residents, Rochelle and Alec, own wells that produce safe drinking water. Each week Rochelle and Alec work together to decide how many gallons of water to pump. They bring the water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Rochelle and Alec can pump as much water as they want without cost so that the marginal cost of water equals zero. The town's weekly demand schedule and total revenue schedule for water is shown in the following table:

Quantity

(Gallons)

Price

(Dollars per gallon)

Total Revenue and Total Profit

(Dollars)

0 60 0
100 55 5,500
200 50 10,000
300 45 13,500
400 40 16,000
500 35 17,500
600 30 18,000
700 25 17,500
800 20 16,000
900 15 13,500
1,000 10 10,000
1,100 5 5,500
1,200 0 0

Refer to Table 18-1. If Rochelle and Alec operate as a profit-maximizing monopoly in the market for water, how many gallons of water will be produced and sold?

Question

Table 18-1
Imagine a small town in which only two residents, Rochelle and Alec, own wells that produce safe drinking water. Each week Rochelle and Alec work together to decide how many gallons of water to pump. They bring the water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Rochelle and Alec can pump as much water as they want without cost so that the marginal cost of water equals zero. The town's weekly demand schedule and total revenue schedule for water is shown in the following table:

​

Quantity

(Gallons)

Price

(Dollars per gallon)

Total Revenue and Total Profit

(Dollars)

0 	60	0
100	55	5,500
200	50	10,000
300	45	13,500
400	40	16,000
500	35	17,500
600	30	18,000
700	25	17,500
800	20	16,000
900	15	13,500
1,000	10	10,000
1,100	5	5,500
1,200	0	0

​

Refer to Table 18-1. If Rochelle and Alec operate as a profit-maximizing monopoly in the market for water, how many gallons of water will be produced and sold?

BlackTom AI · Accepted Answer

First, I’ll restate the scenario and what we’re optimizing. Rochelle and Alec face a demand schedule for water and have zero marginal cost, so the monopoly will produce where marginal revenue (MR) from selling an extra gallon is still positive, and stop where MR would become nonpositive because there’s no cost to produce but selling more would reduce revenue.
Option by option analysis:
- 500 gallons: Between 500 and 600 gallons, the total revenue rises from 17,500 to 18,000, a gain of 500 over 100 gallons. That implies MR for the 500th to 600th gallon is +5. Since MC = 0, producing this extra range increases profit by 5 dollars per 100 gallons, so the firm would happily add this block as long as MR > 0. Therefore, choosing 500 gallons ignores a profitable extra 100 gallons and misses positive MR in the next interval.
- 0 gallons: If the firm produced nothing, it would forego all potential positive revenue. The MR from moving from 0 to 100 gallons is +55 (revenue would rise from 0 to 5,500). With MC = 0, a positive MR means producing would increase profit. Thus, producing 0 gallons is not profit-maximizing.
- 1,200 gallons: From 1,100 to 1,200 gallons, total revenue drops from 5,500 to 0, a large negative change in revenue. The MR for that last interval is -5 or worse in subsequent intervals, indicating producing beyond 600 gallons would reduce revenue. Since MC is zero, you would not push into negative MR territory, because that would lower profit.
- 600 gallons: Look at the progression: from 500 to 600 gallons, TR increases by 500 (from 17,500 to 18,000), so MR over that final 100-gallon step is +5. The next interval, from 600 to 700 gallons, TR decreases by 500 (from 18,000 to 17,500), giving MR = -5. With MC = 0, you maximize profit by producing as long as MR > 0 and stopping before MR turns negative. That boundary occurs after producing 600 gallons, since the following increment would reduce revenue. Therefore, the quantity where MR remains positive up to the last profitable increment is 600 gallons.
- 700 gallons: As noted, the MR for moving from 600 to 700 gallons is negative (-5). Since MC = 0, taking a loss in revenue by expanding output further would reduce profit. Hence 700 gallons is not optimal.
- Other intermediate quantities (e.g., 500 or 1,100) fail to align with the MR=0 crossing point: 500 leaves a positive MR for the next increment, and 1,100 involves producing in a region with negative MR, which would lower profit.

Putting these observations together: with zero marginal cost, the profit-maximizing choice is to produce up to the point where the next increment would yield a nonpositive marginal revenue. The last positive MR occurs for the interval 500–600 gallons (MR = +5), and the next interval 600–700 gallons would give MR = −5. Therefore, the quantity corresponding to the profit-maximizing level of output is 600 gallons.

In summary, each option was assessed against the rule MR > MC (with MC = 0). Options that ignore a remaining positive MR in the next interval (like 500) or that require expanding into a negative MR region (like 700 or 1,200) fail the profit-maximization criterion. The 600-gallon choice satisfies maximizing profit given the MR schedule and zero marginal cost.

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