Consider a monopoly with a production function given by q = f(x) = √x and a fixed cost of $1. The input price is $0.50. The monopolist sells her product in a market that has ten consumers. Let p denote the unit price of the good. Assume that we can represent the preferences of every consumer as follows: If consumer i purchases q units of the good and has y dollars left to spend on all other goods, whose prices are held fixed, the consumer’s utility is √q + kiy, where three of the consumers have ki = 4, four have ki = 3, and three have ki = 2. Each of these ten consumers has $1,000 to spend.

(a) Assuming that the optimal solutions q and y to the consumer’s utility maximization problem are both strictly positive for all ki, find the market demand function that the monopolist faces. (b) Find the profit-maximizing price and quantity for the monopolist.