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Answer to Question #89785 in Microeconomics for Faith

Question #89785
Consider a utility company in a city which is the only licensed water supplier in the city. The demand for water is given by P = 10 - 0.006Q and the marginal cost of the company is given by MC = 2 + 0.004Q. Identify the optimal output, the market price, the consumer surplus, the producer surplus and the deadweight loss in the water market
Expert's answer

The output is optimal, when MR = MC.

MR = TR' = (P×Q) ' = 10 - 0.012Q.

10 - 0.012Q = 2 + 0.004Q,

0.016Q = 8,

Q = 500 units.

At this point P = 2 + 0.004×500 = 4.

The market price P = 10 - 0.006×500 = 7.

The consumer surplus is: CS = 0.5×(10 - 7)×500 = 750.

The producer surplus is: PS = 0.5×(7 - 2)×500 = 1250.

The competitive output is produced at MC = D, so:

10 - 0.006Q = 2 + 0.004Q,

0.01Q = 8,

Q = 800 units.

The deadweight loss in the water market is:

DWL = 0.5×(7 - 4)×(800 - 500) = 450.

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