Aggregate welfare and surplus

The Southern Nevada Water Authority (SNWA) supplies water to Las Vegas. Its cost function for water supply is given by C = 10Q + 8Q2 , where Q is average daily quantity of water supplied, in million gallons. Total daily demand for water in Las Vegas is given by: Q = 515 - 5P, where P is the price of water in dollars per million gallons of water.

(a) Does economic efficiency call for SNWA to follow marginal cost or average cost pricing when setting the price at which it sells water?

(b) If SNWA wants to exactly break even when selling water and not earn any surplus, should it follow marginal or average cost pricing when setting the price at which it sells water?

(c) If SNWA uses marginal cost pricing, what price will it set? How much water will it sell? What is the aggregate consumer's plus producer's surplus that results in this case?

(d) If SNWA uses average cost pricing, what price will it set? How much water will it sell? What is the aggregate consumer's plus producer's surplus that results in this case?

(e) How does the aggregate consumer's plus producer's surplus differ between (c) and (d)? Lecture 10-3 Market allocation and welfare.