Math Problem Statement
Solution
Let's break down and solve each scenario:
Scenario 1: Alice's Jeans Purchase
- Willing to spend: $30
- Price of jeans (pre-discount): $35
- Discount coupon: $10 off
- Actual price paid by Alice: $35 - $10 = $25
Since Alice was willing to spend $30 but only paid $25, she receives a consumer surplus.
- Consumer surplus formula: Willingness to pay - Price paid
- Alice’s surplus: $30 - $25 = $5
Scenario 2: Jeff's Steak Purchase
- Willing to pay: $20
- Price of steak (pre-discount): $16
- Discount: 75% off of $16
- Actual price paid: $16 - (75% of $16) = $16 - $12 = $4
Since Jeff was willing to pay $20 but only paid $4, he receives a consumer surplus.
- Consumer surplus formula: Willingness to pay - Price paid
- Jeff’s surplus: $20 - $4 = $16
Scenario 3: Nicole's Hockey Puck Sale
- Minimum selling price: $500
- Final bid: $501
Since Nicole was willing to sell the puck for $500 but sold it for $501, she receives a producer surplus.
- Producer surplus formula: Final sale price - Minimum selling price
- Nicole’s surplus: $501 - $500 = $1
Summary of Answers
- Alice receives a: Consumer surplus
- Alice’s surplus: $5
- Jeff receives a: Consumer surplus
- Jeff’s surplus: $16
- Nicole receives a: Producer surplus
- Nicole’s surplus: $1
Would you like further details on these calculations? Here are some related questions to deepen your understanding:
- What are other examples of consumer surplus in real life?
- How do discounts affect consumer surplus in general?
- What is producer surplus, and how does it differ from consumer surplus?
- Can a transaction result in both a producer and consumer surplus simultaneously?
- How can producers maximize their surplus when selling goods?
Tip: Consumer surplus increases when consumers can buy a product for less than they are willing to pay.
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Math Problem Analysis
Mathematical Concepts
Consumer Surplus
Producer Surplus
Price Willingness
Discount Calculation
Formulas
Consumer surplus = Willingness to pay - Price paid
Producer surplus = Sale price - Minimum selling price
Discounted price = Original price - (Discount percentage * Original price)
Theorems
Consumer Surplus Theory
Producer Surplus Theory
Suitable Grade Level
Grades 9-12
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