Marginal Cost Pricing

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Marginal Cost Pricing
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P
MC
MR D P
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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.
Lets see how a government that provides water
should operate.
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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.
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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. Lets 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.
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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. Lets 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.