The Big City Fitness Center offers Family and Corporate memberships and is planning to utilize price discrimination to maximize its profits. The estimated weekly demand for the family segment of the market is Q fam. = 984 â 20P, while the corporate segment weekly demand is estimated to be Q corp. = 2,070 â 50P. The Total Cost per week for offering memberships, regardless of type, is T.C. = 12,000 + 10Q.
a) With price discrimination how many memberships should this gym offer in each market segment, and what rate (price) should it charge to each group of customers?
b) What would its weekly profits be?
c) What would the mark-up, as a percentage of the membership price, be in each market segment?
The Big City Fitness Center offers Family and Corporate memberships and is planning to utilize price discrimination to maximize its profits. The estimated weekly demand for the family segment of the market is Q fam. = 984 â 20P, while the corporate segment weekly demand is estimated to be Q corp. = 2,070 â 50P. The Total Cost per week for offering memberships, regardless of type, is T.C. = 12,000 + 10Q.
a) With price discrimination how many memberships should this gym offer in each market segment, and what rate (price) should it charge to each group of customers?
b) What would its weekly profits be?
c) What would the mark-up, as a percentage of the membership price, be in each market segment?
Related textbook solutions
Related questions
1).
A consumer spends more time searching for a good when her reservation price is:
increased.
reduced.
fixed.
None of the statements is correct.
2).
In the game shown below, firms 1 and 2 must independently decide whether to charge high or low prices.
Which of the following are Nash equilibrium payoffs in the one-shot game?
(0, 0)
(5, -5)
(-5, 5)
(10, 10)
3).
A risk-neutral individual would:
prefer $5 with certainty to a risky prospect with the expected value of $5.
prefer a risky prospect with an expected value of $5 to a certain amount of $5.
be indifferent between a risky prospect with an expect value of $5 to a certain amount of $5.
prefer a risky prospect with the expected value of $0.50 to $5 with certainty.
4).
Snowpeak Ski Resort offers a price for a lift ticket that is barely over its marginal cost, but the high equipment rental fee keeps generating big profits. Which pricing strategy is the management using?
Price discrimination
Two-part pricing
Commodity bundling
Cross-subsidization
5).
The short run is defined as the time frame:
in which there are no fixed factors of production.
in which there are fixed factors of production.
less than one year.
less than three years.
6).
Fixed costs exist only in:
the long run.
capital-intensive markets.
the short run.
labor-intensive markets.
7).
Top of Form
Non-fed ground beef is an inferior good. In economic booms, grocery managers should:
increase their orders of non-fed ground beef.
reduce their orders of non-fed ground beef.
not change their orders of non-fed ground beef.
neither increase, reduce, nor maintain their current orders for non-fed ground beef.
Bottom of Form
8).
Which of the following pricing strategies is NOT used in markets with special cost and demand structures?
Peak-load pricing
Cross-subsidization
Transfer pricing
Low-price guarantees
9).
A perfectly competitive firm faces a:
perfectly elastic demand function.
perfectly inelastic demand function.
demand function with unitary elasticity.
None of the answers is correct.
10).
The special demand structure that induces a firm to use a cross-subsidization strategy is:
perfect substitution among products.
imperfect substitution among products.
independent demand for products.
interdependent demand for products.
11).
Which of the following factors reduces the need for government involvement in the marketplace?
The presence of externalities
The incentive to rent-seek
The need for public goods
Incomplete information
12).
Which of the following statements is true?
A mineral rights auction is not the same as a common-value auction.
An auctioneer is always indifferent between different kinds of auctions.
The Dutch and first-price, sealed-bid auctions are strategically equivalent.
An English auction always yields lower expected revenues than a second-price, sealed-bid auction.
13).
Which of the following is true concerning negative externalities?
Firms tend to produce more than the efficient level of output.
Society gains because firms do not pay the external costs of production.
Perfect competition is better than monopoly from the viewpoint of society even in the presence of negative externalities.
With negative externalities, a monopoly will always produce an output level less than is socially efficient.
14).
Which of the following is true under monopoly?
P > ATC
P > MC
P = MR
P = ATC
15).
Differentiated goods are NOT a feature of a:
perfectly competitive market.
monopolistically competitive market.
monopolistic market.
perfectly competitive market and monopolistic market.
16).
Producer surplus is measured as the area
below the demand curve and above the market price.
above the demand curve and below the market price.
above the supply curve and below the market price.
below the supply curve and above the market price.
17).
Jaynet spends $25,000 per year on painting supplies and storage space. She recently received two job offers from a famous marketing firm â one offer was for $105,000 per year, and the other was for $85,000. However, she turned both jobs down to continue a painting career. If Jaynet sells 30 paintings per year at a price of $9,000 each:
a. What are her accounting profits?
$
b. What are her economic profits?
$
18).
You are the manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Group 1âs elasticity of demand is -2, while group 2âs is -4. Your marginal cost of producing the product is $40.
a. Determine your optimal markups and prices under third-degree price discrimination.
Instruction: Round your answers to two decimal places.
Markup for group 1:
Price for group 1: $
Markup for group 2:
Price for group 2: $
b. Which of the following are necessary conditions for third-degree price discrimination to enhance profits.
Instructions: You may select more than one answer. Click the box with a check mark for the correct answers and click twice to empty the box for the wrong answers. You must click to select or deselect each option in order to receive full credit.
| At least one group has elasticity of demand less than one in absolute value. | |
| There are two different groups with different (and identifiable) elasticities of demand. | |
| We are able to prevent resale between the groups. | |
| At least one group has elasticity of demand greater than 1 in absolute value. |
19).
You are the manager of a firm that receives revenues of $60,000 per year from product X and $80,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross-price elasticity of demand between productY and X is -1.4.
How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 2 percent?
Instructions: Round your answer to the nearest dollar. Include a minus (-) sign if applicable.
$
