Please write your answers neatly and legibly.
1. Consider a market that is comprised of two types of buyers whose demand curves are given by the following equations where P is the price per unit in dollars and Q is the number of units of the good:
Demand for Type I buyers: P = 20 – (1/2)Q
Demand for Type II buyers: P = 10 – (1/8)Q
Suppose there is a single producer of this good and the producer's MC is given by the equation:
MC = 2
Assume that this producer has no fixed costs.
a. Suppose that this producer can treat this market as two separate markets: the market for Type I buyers and the market for Type II buyers. Given the above information, calculate the profit maximizing price for Type I buyers, the profit maximizing quantity for Type I buyers, the level of total revenue from Type I buyers, the level of total cost incurred in producing for Type I buyers, and the level of profits from this group of buyers. Show all your work for full credit. Put your answers in the provided spaces.
Price to Type I buyers = ____
Quantity to Type I buyers = _____
Total Revenue from Type I buyers = _____
Total Cost from Type I buyers = _______
Profit from Type I buyers = _______
b. Suppose that this producer can treat this market as two separate markets: the market for Type I buyers and the market for Type II buyers. Given the above information, calculate the profit maximizing price for Type IIbuyers, the profit maximizing quantity for Type II
buyers, the level of total revenue from Type IIbuyers, the level of total cost incurred in producing for Type II buyers, and the level of profits from this group of buyers. Show all your work for full credit. Put your answers in the provided spaces.
Price to Type II buyers = _____
Quantity to Type II buyers = ______
Total Revenue from Type II buyers = ______
Total Cost from Type II buyers = _______
Profit from Type II buyers = _______
c. Suppose that this producer is forced to sell this good to both Type I and Type II buyers as if they are a single market (the producer would be a single price monopolist in this case). Calculate the profit maximizing quantity if the producer combines these two types of buyers into one market.
Then, calculate the profit maximizing price for this market, the total revenue for this single price monopolist, the total cost for this single price monopolist, and the profits for this single price monopolist. Show your work for full credit. Put your answers in the provided spaces.
Price if single price monopolist = _____
Quantity if single price monopolist = ______
Total Revenue if single price monopolist = ______
Total Cost if single price monopolist = _____
Profit if single price monopolist = _____