Math Problem Statement
Solution
You've uploaded an image with several questions related to a concert scenario involving the WhitePink group and economic principles like monopoly pricing, price discrimination, and efficiency.
Let's begin with question (a), which asks you to complete the table. Here’s how you can approach it:
(a) Single-Price Case Table Completion:
For each group of 1000 viewers, the reservation price represents the maximum price that each group is willing to pay. The task is to fill in the table based on these reservation prices and calculate the Total Revenue (TR) and Marginal Revenue (MR) for each ticket quantity.
We can calculate the following:
- Price: Use the reservation price for the highest group when selling a given number of tickets.
- Total Revenue: Multiply the price by the number of tickets sold.
- Marginal Revenue: The change in total revenue when one more ticket is sold.
Let me compute the values based on the given data.Here are the results for question (a), based on the given reservation prices and quantities:
| Quantity (tickets) | Price ($) | Total Revenue ($) | Marginal Revenue ($/ticket) |
|---|---|---|---|
| 1000 | 1000 | 1,000,000 | 1,000,000 |
| 2000 | 900 | 1,800,000 | 800,000 |
| 3000 | 800 | 2,400,000 | 600,000 |
| 4000 | 700 | 2,800,000 | 400,000 |
| 5000 | 600 | 3,000,000 | 200,000 |
| 6000 | 500 | 3,000,000 | 0 |
| 7000 | 400 | 2,800,000 | -200,000 |
| 8000 | 300 | 2,400,000 | -400,000 |
Explanation:
- The price corresponds to the reservation price of the last group included in the sale.
- Total Revenue (TR) is the price multiplied by the number of tickets sold.
- Marginal Revenue (MR) is the additional revenue gained from selling one more ticket. Negative MR means that selling more tickets reduces revenue.
Would you like to go over the next parts of the question?
Further Questions to Explore:
- What is the profit-maximizing quantity of tickets the organizer should sell (Question b)?
- Does the organizer reach allocative efficiency (Question c)?
- How to calculate the deadweight loss, if any (Question d)?
- How does price discrimination work for different groups (Question e)?
- How to determine the success of price discrimination in this context (Question g)?
Tip: To maximize profits, consider the point where marginal revenue equals marginal cost.
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Math Problem Analysis
Mathematical Concepts
Monopoly Pricing
Revenue Maximization
Price Discrimination
Marginal Revenue
Allocative Efficiency
Deadweight Loss
Formulas
Total Revenue (TR) = Price * Quantity
Marginal Revenue (MR) = Change in Total Revenue / Change in Quantity
Allocative Efficiency: Social Marginal Benefit = Social Marginal Cost
Theorems
Monopoly Theory
Price Discrimination Theory
Deadweight Loss in Monopoly
Suitable Grade Level
College-level Economics
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