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Chapter 10: Problem 7

You are the owner of a nail salon. Your female customer's price elasticity of demand for manicures is -2.5 ; your male customer's price elasticity of demand for manicures is -1.2 . The marginal cost of manicuring a customer's nails is \(\$ 12\). a. If you segment the market by gender, what price should you charge women? What price should you charge men? b. Explain intuitively why you should charge each group a different price.

Short Answer

Expert verified
Charge women $6 and men $72. Different elasticities justify these prices.

Step by step solution

01

Understanding Price Elasticity of Demand

Price elasticity of demand measures how the quantity demanded of a good responds to a change in its price. For women, it's -2.5, suggesting high sensitivity; for men, it's -1.2, indicating moderate sensitivity.
02

Using Elasticity in Pricing Strategy

The formula to set the optimal price is \( P = \frac{E}{1+E} \times MC \), where \( E \) is the price elasticity of demand and \( MC \) is the marginal cost. This formula comes from maximizing profit by equating marginal revenue to marginal cost.
03

Calculating the Price for Women

Substitute the given values into the formula for women: \( E_{women} = -2.5 \) and \( MC = 12 \). Thus, \( P_{women} = \frac{-2.5}{1-2.5} \times 12 = 6 \). Therefore, the price charged to women is \$6.
04

Calculating the Price for Men

Substitute the given values into the formula for men: \( E_{men} = -1.2 \) and \( MC = 12 \). Thus, \( P_{men} = \frac{-1.2}{1-1.2} \times 12 = 72 \). Therefore, the price charged to men is \$72.
05

Intuitive Explanation

Since women have a higher elasticity (more sensitive to price change) than men, you should charge women a lower price to increase demand, while men's lower sensitivity allows for a higher price.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Marginal Cost
Marginal cost is a key concept in pricing, as it represents the cost incurred to produce one additional unit or service. In the context of your nail salon, the marginal cost of giving a manicure is $12. Understanding marginal cost is crucial for setting prices that cover production costs while also maximizing profit. It informs the pricing strategy by determining the baseline price from which you can begin to consider demand elasticity adjustments.
In practice, businesses often strive to ensure that the price of their product exceeds the marginal cost. This helps in covering fixed costs and contributing to profit. Marginal costs can vary based on input costs, resource allocation, and efficiencies gained from production.
For example, as a nail salon owner, if your marginal cost is consistently $12 per manicure, knowing this allows you to strategically price your services to not only cover costs but also to segment the market effectively.
Market Segmentation
Market segmentation involves dividing a broader market into subsets of consumers who have common needs and priorities. For your nail salon, this means considering distinct groups, such as women and men, each with their specific price sensitivities. By recognizing that these groups respond differently to price changes, you can tailor your pricing strategy to suit each segment individually.
Here are a few benefits of market segmentation:
  • More precise targeting: By understanding different segments, you can better tailor your marketing efforts and service offerings to meet specific consumer demands.
  • Enhanced customer satisfaction: Offering prices that align with each segment's price sensitivity can increase consumer satisfaction and loyalty.
  • Improved resource allocation: Segmentation allows you to allocate your resources effectively, focusing efforts on the most profitable or the most actionable segments.
Market segmentation using elasticity information helps you set prices that maximize both reach and profitability by acknowledging and capitalizing on differences in customer preferences and willingness to pay.
Pricing Strategy
Pricing strategy is integral to the success of any business since it directly impacts revenue. In the nail salon scenario, the pricing strategy involves using price elasticity of demand to set gender-specific prices. The formula used, \[ P = \frac{E}{1+E} \times MC \]allows you to calculate the optimal price for different groups based on their sensitivity to price changes. This formula considers how sensitive demand is to price changes and suggests that for highly elastic markets (like women with an elasticity of -2.5), a lower price (6) should be set to entice more purchases.
Conversely, for less elastic markets (like men with -1.2 elasticity), a higher price (\$72) can be charged without drastically affecting demand. By understanding these principles, businesses can adjust their prices not just to cover costs but also to maximize profitability across different consumer groups.
When constructing a pricing strategy, it's crucial to consider factors such as competitor pricing, value perception among customers, and overall market conditions, alongside elasticity and marginal costs.

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Most popular questions from this chapter

A local golf course's hired-gun econometrician has determined that there are two types of golfers, frequent and infrequent. Frequent golfers' annual demand for rounds of golf is given by \(Q_{f}=24-0.3 P\), where \(P\) is the price of a round of golf. In contrast, infrequent golfers' annual demand for rounds of golf is given by \(Q_{i}=10-0.1 P\). The marginal and average total cost of providing a round of golf is \(\$ 20\). a. If the golf course could tell a frequent golfer from an infrequent golfer, what price would it charge each type? How many times would each type golf? How much profit would the golf course generate? The greens manager has difficulty telling frequent from infrequent golfers, so she decides to use second-degree price discrimination (quantity discounts) to make different types of golfers self-select into the most profitable pricing scheme. The course sets a price for individual rounds of golf, but also offers a quantity discount for members willing to buy a rather large quantity of rounds in advance. The course's owners hope that frequent golfers will selfselect into the discounted plan, and that infrequent golfers will choose to buy individual rounds. b. What price should the golf course set for individual rounds of golf? Why? c. If the course wishes to maximize profit, what price and minimum quantity should it establish for the discounted plan? d. Which plan will generate the greatest consumer surplus for frequent golfers, the individual-round plan or the discount plan? Illustrate your answer by showing and measuring the areas of surplus on frequent golfers' inverse demand curves. e. Which plan will generate the greatest consumer surplus for infrequent golfers, the individualround plan or the discount plan? Illustrate your answer by showing the areas of surplus on infrequent golfers' inverse demand curves. f. Based on your answers to (d) and (e), will the plan be successful in making golfers self-select into the most profitable plan for the golf course? g. Suppose that each type of golfer came to the course with the word "frequent" or "infrequent" tattooed on his or her forehead. Is this information of any value to the golf course owner? (In other words, can the owner earn any more profits by segmenting than it did with its quantity discount plan?)

Movie theaters often charge substantially less for afternoon showings than for evening showings. Explain how theaters use time of day to segment their customers into low-elasticity and high-elasticity groups.

Promoters of a major college basketball tournament estimate that the demand for tickets on the part of adults is given by \(Q_{a d}=5,000-10 P,\) and that the demand for tickets on the part of students is given by \(Q_{s t}=10,000-100 P .\) The promoters wish to segment the market and charge adults and students different prices. They estimate that the marginal and average total cost of seating an additional spectator is constant at \(\$ 10\) a. For each segment (adults and students), find the inverse demand and marginal revenue functions. b. Equate marginal revenue and marginal cost. Determine the profit-maximizing quantity for each segment. c. Plug the quantities you found in (b) into the respective inverse demand curves to find the profit-maximizing price for each segment. Who pays more, adults or students? d. Determine the profit generated by each segment, and add them together to find the promoter's total profit. e. How would your answers change if the arena where the event was to take place had only 5,000 seats?

Rockway \& Daughters Piano Co. wishes to sell a piano to everyone. But some consumers are budgetconscious, and others are not, and unfortunately, Rockway cannot tell which is which. So, Rockway produces a premium line of pianos that it markets under the Rockway name, and a similar line of pianos that it markets under the Dundee name. While the cost of producing these pianos is quite similar, all consumers agree that Rockway pianos are of higher quality than Dundee pianos, and would be willing to pay more for a Rockway. Budget-conscious consumers feel that Dundee pianos are worth $$ 6,000,\( and Rockways are worth \) 8,000 .\( Performance artists believe that Dundee pianos are worth \)\$ 7,000\( and Rockways are worth $$ 12,000\). a. Suppose Rockway & Daughters prices its Dundee pianos at $$ 5,000\( and its Rockway pianos at $$ 10,500 .\) Are these prices incentive compatible - that is, will more price-conscious consumers purchase the Dundee line, while more performance-oriented players choose the Rockway? Explain. b. How much must Rockway \& Daughters reduce the price of its Rockway line in order to achieve incentive compatibility? c. Suppose instead that Rockway \& Daughters tries to achieve incentive compatibility by raising the price of its Dundee line. Can it do so? And if so, how? d. If you ran Rockway \& Daughters Piano Co., which method would you use to achieve incentive compatibility: the one you outlined in (b), or the one you outlined in (c)? Why?

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