Math Problem Statement

Suppose that Alex and Becky are the only consumers in the Whatville earrings market. The following table represents their annual demand schedules for earrings: Price Alex’s Quantity Demanded Becky’s Quantity Demanded (Dollars per pair) (Pairs) (Pairs) 10 24 48 20 12 32 30 8 24 40 4 16 50 0 8 On the following graph, plot Alex’s demand for earrings using the green points (triangle symbol). Next, plot Becky’s demand for earrings using the purple points (diamond symbol). Finally, plot the market demand for earrings using the blue points (circle symbol). Note: Line segments will automatically connect the points. Remember to plot from left to right. Alex’s Demand Becky’s Demand Market Demand 0 16 32 48 64 80 96 60 50 40 30 20 10 0 PRICE (Dollars per pair) QUANTITY (Pairs)

Solution

To solve this, we'll follow these steps:

  1. Plot Alex's Demand: From the table, Alex's demand at different price points is:

    • At $10: 24 pairs
    • At $20: 12 pairs
    • At $30: 8 pairs
    • At $40: 4 pairs
    • At $50: 0 pairs

  2. Plot Becky's Demand: From the table, Becky's demand at different price points is:

    • At $10: 48 pairs
    • At $20: 32 pairs
    • At $30: 24 pairs
    • At $40: 16 pairs
    • At $50: 8 pairs

  3. Market Demand: The market demand is the sum of Alex's and Becky's quantities at each price point:

    • At $10: 24 (Alex) + 48 (Becky) = 72 pairs
    • At $20: 12 (Alex) + 32 (Becky) = 44 pairs
    • At $30: 8 (Alex) + 24 (Becky) = 32 pairs
    • At $40: 4 (Alex) + 16 (Becky) = 20 pairs
    • At $50: 0 (Alex) + 8 (Becky) = 8 pairs

Now, let's plot the demand curves on the graph:

  • Alex's Demand: Use green triangle symbols for the points (10, 24), (20, 12), (30, 8), (40, 4), and (50, 0).
  • Becky's Demand: Use purple diamond symbols for the points (10, 48), (20, 32), (30, 24), (40, 16), and (50, 8).
  • Market Demand: Use blue circle symbols for the points (10, 72), (20, 44), (30, 32), (40, 20), and (50, 8).

The graph will represent the individual demand schedules (for Alex and Becky) as well as the market demand curve.

Would you like to proceed with a graphical representation, or would you like further details on demand curves and their implications?

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Math Problem Analysis

Mathematical Concepts

Demand Curves
Market Demand
Graphing Data

Formulas

Market Demand = Alex's Demand + Becky's Demand at each price point

Theorems

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Suitable Grade Level

Grades 10-12

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