here's the problem and my solution so far:
In this case, the Marginal Private Benefit (MPB) is given by the equation MPB = 100 - 4q and the Marginal Social Cost (MSC) is given by the equation MSC = 3q.
The market equilibrium occurs where MPB equals MSC, so we can set the two equations equal to each other and solve for q:
100 - 4q = 3q => 7q = 100 => q = 100 / 7 ≈ 14.29
However, there is a positive consumption externality of $40 per unit consumed. This means that the Marginal Social Benefit (MSB) is actually MPB + Externality = (100 - 4q) + 40 = 140 - 4q.
The socially optimal quantity occurs where MSB equals MSC, so we can set these two equations equal to each other and solve for q:
140 - 4q = 3q => 7q = 140 => q = 140 / 7 = 20
The Deadweight Loss (DWL) is the area of the triangle formed by the quantity difference (20 - 14.29) and the price difference ((140 - 420) - (100 - 414.29)). So,
DWL = 0.5 * (20 - 14.29) * ((140 - 420) - (100 - 414.29)) => DWL ≈ \$19.60
So, the deadweight loss that results in the market equilibrium is approximately \$19.60. '
I'm not too sure why this is incorrect. Can anyone give me a hand. Any help will be greatly appreciated.