Government production. Should the government produce as a monopolist or try to act like a competitive firm?. Say the demand for water in a community is Q = 50 –2P. In inverse form we have P = 25 - .5Q.
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Should the government produce as a monopolist or try to act like a competitive firm?
Q = 50 –2P. In inverse form we have P = 25 - .5Q.
If the total cost of production is TC = 100 + 10Q, then marginal cost is of a special form, MC = 10 (a constant).
We have seen the competitive solution is efficient and occurs where P = MC. So we have
25 - .5Q = 10, or Q = 30 and P = 10.
Consumer surplus = .5(15)(30) = $225. There is no producer surplus when MC is horizontal in a competitive situation.
MC = P
Consumer surplus = .5(7.5)(15) = $56.25. Producer surplus =(7.5)(15) = $112.50
MC = P
Note the loss to the consumer is what the producer gains, $112.50, and the deadweight loss triangle on the consumer side, .5(7.5)(15) = 56.25.
Sometimes in problems we work it makes sense to assume AC = MC = some constant dollar amount. Then we can solve for best Q where
P = MC in competition, or
MR = MC in Monopoly (and P is found on demand curve).
Then profit =
(P – AC)Q