A water utility for a growing city is considering expanding their capacity by investing in a larger system of wells. Their long-run marginal cost of water provision is characterized by the function MC(q) = 5 + 2 3 q (q is in thousands of gallons). Current demand is of the form p = 20 − q but future demand is expected to rise to p = 25 − q. The issue facing the utility is one of fixed capacity. With current demand they are already running right at capacity and need to incur investment costs if they are to provide more (i.e., supply becomes perfectly inelastic at the current equilibrium quantity

(a) Determine the current equilibrium price and quantity.

(b) Determine the equilibrium price and quantity that will be in effect once the market experiences “future” demand and the utility makes no capacity expansion investment.

(c) Determine the equilibrium price and quantity that will be in effect once the market experiences “future” demand and the utility expands capacity just enough to meet that demand.

(d) At what cost of investment would the utility be indifferent between the scenarios in (b) and (c), if they are concerned only about maximizing social welfare?