Kathy is attending school in Philadelphia. Each year she returns home to visit her family and friends in New York City. Kathy’s annual demand curve for train tickets from Philadelphia to New York is provided in the accompanying graph. How much benefit does Kathy receive from each trip home? If the price of a round-trip ticket is $230, how many trips should Kathy take?
The Correct Answer and Explanation is:
To answer your question about Kathy’s benefit from each trip home and how many trips she should take given the ticket price of \$230, I’ll walk through the economic concepts involved.
Step 1: Understanding Kathy’s Benefit per Trip — Consumer Surplus
Kathy’s benefit from each trip is measured by consumer surplus, which is the difference between what she is willing to pay and what she actually pays.
- Kathy’s demand curve shows the maximum price she is willing to pay for each additional trip.
- The price of the round-trip ticket is \$230.
- If the price is less than or equal to the maximum willingness to pay for a trip, Kathy gains consumer surplus.
- If the price is higher than her willingness to pay, she won’t take that trip.
Step 2: Determining How Many Trips Kathy Should Take
Kathy should buy tickets up to the point where her willingness to pay equals the price of \$230.
- On the demand curve, find the number of trips for which Kathy’s maximum willingness to pay is at least \$230.
- Trips where willingness to pay < \$230 should not be taken, as the cost exceeds her perceived benefit.
Step 3: Calculate the Total Consumer Surplus (Benefit)
- The consumer surplus is the area between the demand curve and the price line (up to the number of trips purchased).
- It represents the total benefit Kathy receives from the trips after paying the cost of tickets.
Without the actual graph data, here’s a general example of how you would calculate it:
- Suppose Kathy is willing to pay \$300 for her first trip, \$270 for her second, \$240 for her third, and \$210 for her fourth.
- The price is \$230, so she should take 3 trips (since the fourth trip’s willingness to pay, \$210, is less than \$230).
- Consumer surplus per trip would be:
| Trip Number | Willingness to Pay | Price Paid | Surplus per Trip |
|---|---|---|---|
| 1 | \$300 | \$230 | \$70 |
| 2 | \$270 | \$230 | \$40 |
| 3 | \$240 | \$230 | \$10 |
- Total consumer surplus = \$70 + \$40 + \$10 = \$120
Final answers based on the explanation:
- Number of trips Kathy should take: 3 (trips where her willingness to pay ≥ \$230)
- Benefit Kathy receives (total consumer surplus): \$120
Why is this important?
Understanding consumer surplus helps in measuring how much value or benefit consumers derive from purchasing goods or services at a certain price. Kathy maximizes her benefit by choosing trips where the value (willingness to pay) exceeds the cost (ticket price). Buying trips beyond that point would result in negative surplus (loss), so she avoids those. This is a classic example of how individuals make rational economic decisions based on price and personal valuation.
If you can share the actual demand curve or specific data points, I can give you the exact number of trips and the precise benefit Kathy gets.