Asked by Svetlana Stetsenko on May 15, 2024
Verified
A careful analysis of demand for Bubbles in Strasburg, North Dakota, reveals a strange segmentation in the market.(Recall Bubbles is the beverage which produces an unexplained craving for Lawrence Welk's music.It is produced by the process Q minR/5, W , where R is the number of pulverized Lawrence Welk records and W is gallons of North Dakota well water.PR $1, PW $4.) If demand for Bubbles by senior citizens is described by Q0 500P3/2 while demand by those under 65 years old is Qy 50P5, how should Bubbles be priced to maximize profits?
A) $13 for all citizens of Strasburg
B) $9 for senior citizens and $30 for those younger
C) $27 for senior citizens and $11.25 for those younger
D) $13.50 for senior citizens and $45 for those younger
E) $60 for senior citizens and $25 for those younger
Demand Segmentation
The process of dividing a market into distinct groups of buyers with different needs, characteristics, or behaviors.
Bubbles
Economic cycles characterized by rapid expansion followed by a contraction, often driven by speculative or unsustainable growth.
Maximize Profits
The process of determining the best price and output level that leads to the highest possible profit for a business.
- Gain an understanding of how factors such as production constraints and input expenditures affect production and pricing approaches in monopolistic settings.
- Examine how demand distinctions based on demographic factors influence monopolistic price discrimination.
Verified Answer
To find marginal revenue, we need to differentiate the demand functions with respect to quantity, and then multiply by the price:
For senior citizens:
MR1 = (d/dQ) [500P(13/2 - P)] * P = 500(13/2 - 2P)
For those under 65:
MR2 = (d/dQ) [50P(15 - P)] * P = 50(15 - 2P)
Setting MR1 = MC and solving for P gives:
500(13/2 - 2P) = 5
P1 = $11.25
Setting MR2 = MC and solving for P gives:
50(15 - 2P) = 5
P2 = $27.00
Therefore, the optimal pricing strategy is to charge senior citizens $11.25 per bottle and those under 65 years old $27.00 per bottle. Option C is the correct answer.
Learning Objectives
- Gain an understanding of how factors such as production constraints and input expenditures affect production and pricing approaches in monopolistic settings.
- Examine how demand distinctions based on demographic factors influence monopolistic price discrimination.
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