Consider the market for first-aid training classes. Market demand is given by P = 600 – Q. Market supply is given by P = Q. Individuals who have received first-aid training are very helpful in some urgent situations which is captured in a positive spillover, or externality, equal to Q/4. This is thus an external benefit related to the consumption of first-aid training. What is the deadweight loss if the externality is not dealt with?

To calculate the deadweight loss, we first need to find the socially optimal quantity (Q*) where the social benefit equals the social cost.

1. The social benefit is the sum of the private benefit (the demand curve) and the external benefit. The demand curve is given by P = 600 - Q, and the external benefit is given by Q/4. So, the social benefit is given by P = 600 - Q + Q/4.

2. The social cost is the same as the private cost (the supply curve), which is given by P = Q.

3. Setting the social benefit equal to the social cost gives us 600 - Q + Q/4 = Q. Solving this equation for Q gives us Q* = 480.

4. The quantity in the market without considering the externality (Qm) is where the private benefit equals the private cost, or 600 - Q = Q. Solving this equation for Q gives us Qm = 300.

5. The deadweight loss is the area of the triangle formed by Q*, Qm, and the demand curve. The base of the triangle is Q* - Qm = 480 - 300 = 180. The height of the triangle is the difference in price at Q* and Qm, which is (600 - Q*) - (600 - Qm) = Qm - Q* = 300 - 480 = -180.

6. The area of a triangle is 1/2 * base * height, so the deadweight loss is 1/2 * 180 * -180 = -16,200.

However, deadweight loss cannot be negative, so there must be a mistake in the calculation. The mistake is in the calculation of the height of the triangle. The price at Q* is higher than the price at Qm, so the height of the triangle should be Q* - Qm, not Qm - Q*.

Correcting this gives us a height of 480 - 300 = 180, and a deadweight loss of 1/2 * 180 * 180 = 16,200.