Consider a monopoly with a production function given by q = f(x) = x and a fixed

Question

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.

Explanation / Answer

Ans:(a) inverse demand function that monopoly face will be an addition of all demand that each consumer demand. each consumer will spend $1000 on both goods but since given utility function, all consumer will spend all money on both goods, but three consumers will keep their money because money gives more utility.

(b) In equilibrium monopoly will charge $1 and sell quantity 7000

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.