Classwork 5

Public Goods in Action

Part 1 — Conceptual Warm-Up

1. Explain in your own words why public goods require vertical summation of marginal benefits.
   
2. In the Doug–Sasha forest preservation example, what condition makes 10 acres optimal?
   
3. Give one local and one global example of an environmental public good not listed in the lecture.

Part 2 — Applied Problem

Suppose two people, Alex and Jamie, value urban tree planting as follows:

\[ MB_{Alex}(Q) = 16 - Q \quad \quad MB_{Jamie}(Q) = 12 - 2Q \]

(Values are in dollars; truncate at zero.)
The marginal cost of planting trees is constant at $10 per tree.

Tasks:
1. Draw the MB curves for Alex and Jamie separately.
2. Construct the social MB curve by vertical summation.
3. Find the optimal number of trees Q* where SMB = MC.
4. Compare the total benefits received by Alex vs. Jamie at Q.
5. Propose two possible cost-sharing rules (e.g., equal split, benefit-based) and discuss whether each is fair* and/or efficient.

Part 3 — Sensitivity

1. Suppose the cost per tree rises from $10 to $12. Recalculate Q*.
   
2. Suppose Jamie’s valuation increases to \(MB_{Jamie}(Q) = 15 - 2Q\). How does this change Q*?
   
3. Which change (higher cost vs. higher demand) has a larger effect on optimal provision? Why?

Part 4 — Reflection

• How does this exercise illustrate the free-rider problem?
  
• What role should government play when preferences and benefits differ across individuals?