Question

Students receive two types of benefits from standardized test preparation services: first, they learn useful material; second, they score better on the test relative to other students. Because relative performance matters, their improved performance creates a negative externality for other students. Suppose that the inverse market demand function for test preparation services is $P = 60 - 2Q$, where $Q$ is millions of hours of services and $P$ is the price per hour. Suppose also that the market for these services is competitive and that the inverse market supply function is $P = 15 + 0.5Q$. Finally, suppose that the external cost of test preparation is given by $EC = 5Q + 0.75Q^2$. What tax would induce socially optimal behavior?

          Students receive two types of benefits from standardized test
preparation services: first, they learn useful material; second, they score
better on the test relative to other students. Because relative
performance matters, their improved performance creates a negative
externality for other students. Suppose that the inverse market demand
function for test preparation services is $P = 60 - 2Q$, where $Q$ is
millions of hours of services and $P$ is the price per hour. Suppose also
that the market for these services is competitive and that the inverse
market supply function is $P = 15 + 0.5Q$. Finally, suppose that the
external cost of test preparation is given by $EC = 5Q + 0.75Q^2$. What
tax would induce socially optimal behavior?

Students receive two types of benefits from standardized test
preparation services: first, they learn useful material; second, they score
better on the test relative to other students. Because relative
performance matters, their improved performance creates a negative
externality for other students. Suppose that the inverse market demand
function for test preparation services is P = 60 - 2Q, where Q is
millions of hours of services and P is the price per hour. Suppose also
that the market for these services is competitive and that the inverse
market supply function is P = 15 + 0.5Q. Finally, suppose that the
external cost of test preparation is given by EC = 5Q + 0.75Q^2. What
tax would induce socially optimal behavior?

Added by Abigail C.

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