(Some) National Park fees are too low (during peak visitation seasons)

The title above should have been the title to yesterday's post. Here is a recreation demand problem for my students posted over at my course blog:

Given:

• MB = 100 - Q
• MC = TC + CC
• CC = Q - 50
• TC = 10

where MB is marginal benefit, Q is recreation visits, MC is marginal cost, TC is travel cost and CC is congestion cost. Answer the following questions:

1. How many visits would result without a fee?
2. What is the consumer surplus associated with these visits?
3. What is the efficient fee?
4. How many visits would result with the fee?
5. After the fee:
   a. What is the consumer surplus?
   b. What is the government revenue?
   c. What is the deadweight loss?
   d. What are the avoided congest costs?
6. What are the net benefits of the fee policy?

The answers are in the comments at my course blog.

One thing had me awake this morning at 5:00. Why do we add the travel costs and congestion costs to get the marginal (social cost) curve since the recreation manager doesn't care about the (private) travel cost? The answer is because the efficient resource allocation should incorporate all of the benefits and costs. Am I right?

I have these crises of confidences all the time.