### 7. A Model of Price DiscriminationKevin owns a plot of land in the desert that isn't worth much. One day, a giant meteorite falls on his property, creating a large crater. This event attracts scientists and tourists, prompting Kevin to sell nontransferable admission tickets to the meteor crater for both types of visitors: scientists (Market A) and tourists (Market B). The following graphs show daily demand (D) curves and marginal revenue (MR) curves for the two markets. Kevin’s marginal cost of providing admission tickets is zero.#### Graphs Explanation:##### Market A- **Axes**: The x-axis represents the quantity of admission tickets, ranging from 0 to 10. The y-axis represents the price per ticket in dollars, ranging from 0 to 20.- **Demand Curve (DA)**: A downward sloping line from the intercept at $20 on the y-axis to a quantity of 10 on the x-axis.- **Marginal Revenue Curve (MRA)**: A steeper downward sloping line than the demand curve, starting at the same price level of $20 but dropping more quickly.##### Market B- **Axes**: Similar to Market A, with the x-axis for quantity of tickets (0 to 10) and the y-axis for price per ticket (0 to 20).- **Demand Curve (DB)**: Similar to Market A, a downward sloping line starting at $20, moving to a quantity of 10.- **Marginal Revenue Curve (MRB)**: Steeper than the demand curve, starting at $20 but with a more rapid decline.Below these graphs, a scenario is proposed:Suppose that at first, Kevin charges the same price of $8 per admission in both markets so that the total number of admissions demanded is _______ tickets. ### Price Discrimination and Revenue Optimization#### Diagrams Explained:The image contains two graphs labeled as graphs for Market A and Market B, respectively. - **Graph (Market A):** - Horizontal axis: Quantity (Admission tickets) from 0 to 10. - Vertical axis: Price ($) from 0 to 8. - A demand curve (DA) is shown, starting at $8 for 0 tickets and sloping down to $0 at 10 tickets. - A marginal revenue curve (MRA) intercepts the horizontal axis at around 5 tickets.- **Graph (Market B):** - Similar axes to Market A. - A demand curve (DB) starts at $8 for 0 tickets, sloping downwards to $0 at 10 tickets. - A marginal revenue curve (MRB) intercepts the horizontal axis at around 7 tickets.#### Instructions:1. **Pricing Policy Questions:** - Kevin initially charges $8 per admission in both markets. You need to determine the total number of tickets demanded. - For maximizing revenue through different pricing in each market, find the optimal prices and total ticket quantity.2. **Revenue Calculation:** - Complete the table by calculating total revenue for both nondiscriminatory and discriminatory pricing strategies.3. **Price Elasticity Insight:** - Identify in which market Kevin charges a lower price based on price elasticity of demand.#### Table for Completion:| Pricing Policy | Total Revenue (Dollars) ||---------------------|-------------------------|| Nondiscriminatory | || Discriminatory | |#### Conclusion:Understanding the differential pricing strategy and its effects on demand and revenue is essential for optimizing market performance. Consider the elasticity differences when setting prices to ensure maximum profitability.

The demand curve shows the relationship between price and quantity demanded. The negative slope of the curve indicates that price and quantity demanded are inversely related. Marginal revenue is the change in total revenue resulting from the sale of one more unit of the output. The revenue is maximized when the marginal revenue is equal to zero.At a price of $8, the quantity demanded in market A is 6 units and the quantity demanded in market B is 2 units. Therefore the total number of tickets demanded is 8 tickets. To maximize the revenue, the output should be sold upto the level where the marginal revenue is zero. In market A, the marginal revenue is zero when the output is 5 units. The maximum willingness to pay at 5 units is $10. Therefore the price that has to be charged in market A is $10. In market B, the revenue is maximized at 3 units and the price is $6. Therefore the price to charge in market A is $10 and in market B is $6. The total quantity sold at these prices is 8 tickets. Total revenue is the product of price and quantity. The total revenue with and without price discrimination is calculated as, Total revenue without discrimination=Price×Quantity=$8×8=$64Total revenue with discrimination=Price×Quantity=$10×5+$6×3=$68 The total revenue without price discrimination is $64 and the total revenue with price discrimination is $68. When the demand is relatively elastic, the change in quantity demanded is more than proportionate to the change in price. Therefore a small decrease in the price will increase the quantity demanded by a larger amount and the total revenue will increase. Hence to increase the revenue, a lower price should be charged in the market with relatively high elasticity demand.

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7. A model of price discrimination Kevin owns a plot of land in the desert that isn't worth much. One day, a giant meteorite falls on his property, making a large crater. The event attracts scientists and tourists, and Kevin decides to sell nontransferable admission tickets to the meteor crater to both types of visitors: scientists (Market A) and tourists (Market B). The following graphs show daily demand (D) curves and marginal revenue (MR) curves for the two markets. Kevin's marginal cost of providing admission tickets is zero. (? Market A Market B 20 20 18 18 16 16 14 14 12 12 10 10 2 MR, B MR 1 2 3 4 5 6 7 8 10 1 2 3 4 5 6 7 8 10 QUANTITY (Admission tickets) QUANTITY (Admission tickets) PRICE (Dollars per ticket) PRICE (Dollars per ticket)

7. A model of price discrimination Kevin owns a plot of land in the desert that isn't worth much. One day, a giant meteorite falls on his property, making a large crater. The event attracts scientists and tourists, and Kevin decides to sell nontransferable admission tickets to the meteor crater to both types of visitors: scientists (Market A) and tourists (Market B). The following graphs show daily demand (D) curves and marginal revenue (MR) curves for the two markets. Kevin's marginal cost of providing admission tickets is zero. (? Market A Market B 20 20 18 18 16 16 14 14 12 12 10 10 2 MR, B MR 1 2 3 4 5 6 7 8 10 1 2 3 4 5 6 7 8 10 QUANTITY (Admission tickets) QUANTITY (Admission tickets) PRICE (Dollars per ticket) PRICE (Dollars per ticket)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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