Answer

Solution

1. 1

   Aggregate (vertical) marginal benefit is

2. 2
   $$\sum MB = 5(100 - 0.5Q) + 10(50 - 0.25 Q) \quad \text{(while both groups have positive } MB).$$
3. 3

   But each group's $MB$ becomes zero at:

4. 4

   \begin{itemize}[leftmargin=*]

5. 5
   • $MB_H = 0 \Rightarrow Q = 200$,
6. 6
   • $MB_L = 0 \Rightarrow Q = 200$.
7. 7

   \end{itemize}

8. 8

   Both groups have positive $MB$ for $Q < 200$. So,

9. 9
   $$\sum MB = 500 - 2.5 Q + 500 - 2.5 Q = 1000 - 5 Q.$$
10. 10

    Setting $\sum MB = MC$ (Samuelson condition for socially optimal $Q$):

11. 11
    $$1000 - 5 Q = 25 \;\Longrightarrow\; Q = 195.$$

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