1. 1 Government production Should the government produce as a monopolist or try to act like a competitive firm?

2. 2 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. P Q MC = P D 10 30 25 Consumer surplus =.5(15)(30) = $225. There is no producer surplus when MC is horizontal in a competitive situation.

3. 3 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 P Q MC = P D 10 30 25 Consumer surplus =.5(7.5)(15) = $56.25. Producer surplus =(7.5)(15) = $112.50 MR 15 17.5

4. 4 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.

5. 5 Note 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