The market marginal benefit curve for water (measured in thousands of gallons) is MB = 300-Q, where MB is the marginal benefit of water, and Q is thousands of gallons of water each period. The marginal cost of providing the water (including treatment, pumping, and other costs) is MC = .5Q. There are no fixed costs. Suppose that the government utility that provides water service has set the price at $100 per thousand gallons, and supplies 200 thousand gallons.
What is the total benefit of that amount of water?
What is the total cost of providing that amount of water?
What is the net benefit (total benefits minus total costs) of that amount of water?
Are net benefits maximized at 200 thousand gallons? If yes, why? If not, how many gallons should be supplied to maximize net benefits?