Henni runs a hip hairdressing business. Two types of customers come to see Henni -women and men. The demand for haircuts by men is given by QDM = 10 - P, while thedemand for haircuts by women is given by QDW = 102 - P. Assume that the marginal costof haircuts is constant at $2 and is the same for both women and men.a) If Henni operates as a monopolist in her neighborhood and can price discriminatebetween males and females. What profit maximizing price should she charge herfemale customers? What is the profit maximizing price she should charge her malecustomers? What is social welfare under Henni's discriminatory regime?
Question
Henni runs a hip hairdressing business. Two types of customers come to see Henni -women and men. The demand for haircuts by men is given by QDM = 10 - P, while thedemand for haircuts by women is given by QDW = 102 - P. Assume that the marginal costof haircuts is constant at $2 and is the same for both women and men.a) If Henni operates as a monopolist in her neighborhood and can price discriminatebetween males and females. What profit maximizing price should she charge herfemale customers? What is the profit maximizing price she should charge her malecustomers? What is social welfare under Henni's discriminatory regime?
Solution
To solve this problem, we need to find the profit-maximizing price for both men and women.
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For men, the demand function is QDM = 10 - P. To maximize profit, Henni should set the price equal to the marginal cost. So, we have:
P = MC P = $2
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For women, the demand function is QDW = 102 - P. Again, to maximize profit, Henni should set the price equal to the marginal cost. So, we have:
P = MC P = $2
Therefore, Henni should charge both her male and female customers $2 for a haircut to maximize her profits.
Social welfare is the sum of consumer surplus and producer surplus. In this case, since the price is equal to the marginal cost, the entire area under the demand curve up to the quantity sold is consumer surplus, and there is no producer surplus. Therefore, social welfare is maximized.
Please note that this solution assumes that Henni can perfectly price discriminate, i.e., she can charge each customer their maximum willingness to pay. In reality, this is often not possible due to a variety of factors, including imperfect information and the potential for customer backlash.
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