Math Problem Statement

For each scenario, determine whether it results in a producer or consumer surplus. Then calculate the resulting surplus. 1. Alice is willing to spend $30 on a pair of jeans and has a coupon for $10 off. She purchases a pair of jeans that costs $35 pre-discount. 2. Jeff finds steak in the supermarket priced at $16 but that he would have been willing to pay $20 for. The butcher notices the meat is near the expiration date and gives him an extra 75% off. 3. Nicole has a hockey puck from the 2018 Winter Olympic Games and puts it up for sale on eBay. She will only sell the puck if the winning bid is greater than or equal to $500. After the bidding closes, the last bid stands at $501.

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

  1. Alice receives a: Consumer surplus
    • Alice’s surplus: $5
  2. Jeff receives a: Consumer surplus
    • Jeff’s surplus: $16
  3. 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:

  1. What are other examples of consumer surplus in real life?
  2. How do discounts affect consumer surplus in general?
  3. What is producer surplus, and how does it differ from consumer surplus?
  4. Can a transaction result in both a producer and consumer surplus simultaneously?
  5. 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