Suppose the market for household drinking water in San Francisco is modeled as follows:

S = MSC = 10 + 0.2Q

D = MSB = 40 − 0.4Q, 

where Q is millions of gallons per day and MSC and MSB are in cents per gallon.

a. Assuming the city officials use a flat fee pricing system for drinking water, find the equilibrium amount of water that households in San Francisco would use.

b. Suppose instead that officials set the price of water to reflect the true marginal social costs of production. Show that such an approach promotes water conservation by determining the equilibrium quantity, and find the price that must be set to achieve this outcome.