Math Problem Statement

Suppose that Alex and Becky represent the only two consumers of jeans in some hypothetical market. The following table presents their annual demand schedules for jeans: Price Alex’s Quantity Demanded Becky’s Quantity Demanded (Dollars per pair) (Pairs) (Pairs) 10 32 64 20 20 48 30 12 32 40 4 24 50 0 16 On the following graph, plot Alex’s demand for jeans using the green points (triangle symbol). Next, plot Becky’s demand for jeans using the purple points (diamond symbol). Finally, plot the market demand for jeans using the blue points (circle symbol). Note: Line segments will automatically connect the points. Remember to plot from left to right.

Solution

To plot the demand schedules for Alex, Becky, and the total market, follow these steps:

Step 1: Create the Axes

  • X-axis (Horizontal): Represents the price per pair of jeans (in dollars).
  • Y-axis (Vertical): Represents the quantity of jeans demanded (in pairs).

Step 2: Plot Alex's Demand (Green Triangle Points)

Using the table for Alex's demand:

  • At a price of $10, Alex demands 32 pairs.
  • At a price of $20, Alex demands 20 pairs.
  • At a price of $30, Alex demands 12 pairs.
  • At a price of $40, Alex demands 4 pairs.
  • At a price of $50, Alex demands 0 pairs.

Plot these points with green triangles.

Step 3: Plot Becky's Demand (Purple Diamond Points)

Using the table for Becky's demand:

  • At a price of $10, Becky demands 64 pairs.
  • At a price of $20, Becky demands 48 pairs.
  • At a price of $30, Becky demands 32 pairs.
  • At a price of $40, Becky demands 24 pairs.
  • At a price of $50, Becky demands 16 pairs.

Plot these points with purple diamonds.

Step 4: Plot the Market Demand (Blue Circle Points)

The market demand is the sum of Alex's and Becky's demands at each price:

  • At a price of $10: Alex's demand (32) + Becky's demand (64) = 96 pairs.
  • At a price of $20: Alex's demand (20) + Becky's demand (48) = 68 pairs.
  • At a price of $30: Alex's demand (12) + Becky's demand (32) = 44 pairs.
  • At a price of $40: Alex's demand (4) + Becky's demand (24) = 28 pairs.
  • At a price of $50: Alex's demand (0) + Becky's demand (16) = 16 pairs.

Plot these points with blue circles.

Final Graph

The graph will show the three demand curves:

  • Alex's demand curve (green triangles) should slope downward from left to right, showing that Alex's demand decreases as the price increases.
  • Becky's demand curve (purple diamonds) will also slope downward but be higher than Alex's curve at each price.
  • The market demand curve (blue circles) will be the sum of both individual demands and also slope downward.

If you need me to generate this plot for you visually, feel free to upload a picture or clarify!

Would you like any additional details or help with further steps?


Related Questions:

  1. How do shifts in individual demand curves affect the market demand?
  2. What factors could cause a shift in Alex's demand for jeans?
  3. What happens if a third consumer enters the market with their own demand schedule?
  4. How would a price ceiling impact the demand for jeans in this market?
  5. What is the elasticity of demand for each consumer, and how can it be calculated?

Tip:

To determine the market demand at any price level, always sum the quantities demanded by all consumers in the market.

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Math Problem Analysis

Mathematical Concepts

Demand Schedule
Market Demand
Graph Plotting
Summation

Formulas

Market Demand = Sum of Individual Demands at each Price

Theorems

Law of Demand

Suitable Grade Level

Grades 9-12