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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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Government production

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.

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.

P

25

10

MC = P

D

Q

30


If the government acts as a monopoly it would want to produce where MR = MC and charge the price on the demand curve for the quantity. Since the demand for water in a community is Q = 50 –2P. In inverse form we have P = 25 - .5Q, so MR = 25 – 1Q. MR = MC means 25 – 1Q = 10, or Q = 15 and so P = 17.5

Consumer surplus = .5(7.5)(15) = $56.25. Producer surplus =(7.5)(15) = $112.50

P

25

17.5

10

MC = P

MR

D

Q

30

15


So, if the government prices as a monopoly the gain to them is $112.50 in surplus, but the loss to the consumer is 56.25 – 225 = -$168.75.

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.


Note is $112.50 in surplus, but the loss to the consumer is 56.25 – 225 = -$168.75.

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


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