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? [Round your answer to 2 decimal places when needed]
Question
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?
[Round your answer to 2 decimal places when needed]
Solution
To calculate the deadweight loss, we first need to find the socially optimal quantity (Q*) where the social benefit equals the social cost.
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The social benefit is the sum of the private benefit (the demand curve) and the external benefit. The demand curve is P = 600 - Q and the external benefit is Q/4. So, the social benefit is P = 600 - Q + Q/4.
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The social cost is just the supply curve, which is P = Q.
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Set the social benefit equal to the social cost to find Q*:
600 - Q + Q/4 = Q 600 = 5/4Q Q* = 480
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Now, find the price at Q* from the supply curve (since the supply curve represents the social cost in this case):
P* = Q* = 480
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The quantity at the market equilibrium (Qm) is where the demand curve equals the supply curve:
600 - Q = Q Qm = 300
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The price at Qm from the supply curve is:
Pm = Qm = 300
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The deadweight loss is the area of the triangle formed by Qm, Q*, and the demand curve. It's calculated as:
DWL = 0.5 * (Q* - Qm) * (P* - Pm) DWL = 0.5 * (480 - 300) * (480 - 300) DWL = 0.5 * 180 * 180 DWL = 16200
So, the deadweight loss if the externality is not dealt with is 16200.
Similar Questions
Consider the market for first-aid training class.Market demand is given byP=600-Q Market supply is given by P=Q Individuals who have received first-aid training are very helpful in someurgent situations.More specifcally,first-aid training will generate apositive spillover equal to 3/4Q What is the deadweight loss if the extemality is not dealt with? DWM=40,500 None of the other answers is correct DW1=20,250 DWM=40.000 DWL=20,000
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