Athos, Porthos, and Aramis each like to take fencing lessons. The price of a fencing lesson is $10. Athos values a lesson at $17, Porthos at $15, and Aramis at $12. Suppose that if the government taxes fencing lessons at $3 each, the price will rise to $13. A consequence of the tax is that consumer surplus shrinks by
A)$3 and tax revenues increase by $9, so there is a deadweight loss of $3.
B)$6 and tax revenues increase by $9, so there is no deadweight loss.
C)$9 and tax revenues increase by $6, so there is no deadweight loss.
D)$9 and tax revenues increase by $6, so there is a deadweight loss of $3.

Question

Quizplus · Accepted Answer

Before the tax, consumer surplus is the difference between what each person values the lesson at and the price they pay. After the tax, the price increases to $13, and Aramis no longer buys a lesson because it exceeds his valuation. Thus, consumer surplus decreases by $3 for Athos (from $7 to $4), by $2 for Porthos (from $5 to $3), and by $2 for Aramis (from $2 to $0 because he stops buying). This totals a $7 decrease in consumer surplus, not $9. However, tax revenues increase by $6 ($3 from each of the two who still buy lessons), and since the decrease in consumer surplus ($7) plus the tax revenue ($6) does not equal the original surplus ($9), there is a deadweight loss, but the calculation provided in the explanation for the choices is incorrect. The correct approach to determine the deadweight loss involves considering the change in consumer surplus, producer surplus, and tax revenue, but none of the provided choices accurately reflects the correct calculation based on the information given. My initial explanation contained a mistake in calculating the decrease in consumer surplus and in explaining the deadweight loss. The correct explanation for deadweight loss involves the loss in efficiency in the market due to the tax, which is not accurately captured by any of the choices as they are based on incorrect calculations or premises.

Athos, Porthos, and Aramis Each Like to Take Fencing Lessons