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$ P MC MR = D = P
On the previous screen is a picture of a firm in a competitive environment that is a price taker. The firm operates in a market where the price is P. So, we saw before this means the MR = P = the demand line for the firm. The production rule said go to the quantity where the MR = MC (and we assume the operating rule says operate.) So, on the last unit produced the price of the output (which is not under the control of the producer) is made equal to the marginal cost of output. Thus, all the units that have marginal cost less than price are made and on the last unit P = MC. This story we saw was based on the idea that the firm is after maximum profit. Let’s see how a government that provides water should operate.
Say a town has several sources for water that it then sells to people who live and work in the city. The water comes from 3 sources. 1) Water from an underground spring that has a 1 million gallon a day capacity and it costs the city 0.2 cents per gallon to get the water into usable form (this is less than a penny per gallon.) 2) Water from a nearby lake that has a capacity of 2 million gallons a day and it costs the city 0.8 cents per gallon to get the water into a useable form. 3) Water from the ocean in an unlimited capacity and it costs the city 4.0 cents per gallon to get the water into a useable form.
From the low hanging fruit principle you and I know the city will get water first from the spring and then will go to the lake and ocean only if it needs that much on a daily basis. Say consumers want to use 4 million gallons a day when the price is 4 cents a day. Thus a price of 4 cents a day will mean P = MC. Let’s say it can be determined that neighborhoods A, B, and C actually get the water that comes from the spring, neighborhoods D, E, and F actually get the water that comes from the lake and the rest get the water from the ocean. So, say we have 4 million gallons currently being used. How much would cost change if a household in neighborhood A used 1 gallon of water less per day? If the household used 1 less gallon of water, the city would be able to reduce the amount of water it takes from the ocean by 1 gallon and thus cost would fall by 4 cents. This is the marginal cost of water even though the household using 1 less gets its water from the spring.
As long as demand is over 3 million gallons the MC of water is 4 cents and the city should charge 4 cents per gallon of water. Let’s see why charging less than 4 cents per gallon to those folks who get their water from the spring is a bad move. Say the city charges 0.2 cents per gallon to those in neighborhoods A, B, and C. We know from the incentive principle people will use water up to the point where the marginal benefit equals the marginal cost. If the cost to some is 0.2 cents per gallon those people will use more gallons than they would if the price was 4 cents per gallon. So if some only pay 0.2 cents per gallon demand will be even greater than 4 million gallons. So some folks would buy gallons that have a value to them of 0.2 cents but it cost the city at the margin 4 cents to make. Society would lose 3.8 cents of surplus value on those units. So, even the government should charge a P = MC of production.
