Suppose that historically, P&G's prospective toothpaste buyers could be broken into two segments based on income: low income and high income. The daily demand curve for each market segment is summarized below.

Low Income:

Demand Curve: P_L = 2.04-0.008Q_L

Marginal Revenue: MR_L = 2-0.016Q_L

where P_L price paid by low-income customers

Q_L = quantity sold to low-income customers

High Income:

Demand Curve: P_H = 5-0.01Q_H

Marginal Revenue: MR_H = 5-0.02Q_H

where P_H = price paid by high-income customers

Q_L = quantity sold to high-income customers

If the market was not segmented, the demand curve for the overall markets would be:

Demand Curve: P = (755-Q)/225

Marginal Revenue: MR = (755-2Q)/225

where P = price paid by all customers

Q = quantity sold to all customers

The total daily cost of producing toothpaste is TC =5 + Q_L + Q_H

1. (3 points) Suppose P&G is able to segment the market, essentially offering a separate price to each of the market segments by selectively distributing coupons. What is the optimal quantity of toothpaste sold to low-income customers?What is the optimal price that these customers should be charged? What is the optimal quantity of toothpaste sold to high-income customers? What is the optimal price that these customers should be charged? What is P&G's profit across the two market segments?Be sure to show your work, including all calculations and conditions used.

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