Question
It is given that Qd = 300 - P, Qs = Q/2. Government
imposes specific tax in such a way that it maximizes the total tax revenue. Then find out the DWL in such a situation.Solution
We know that when tax is imposed, Pd = Ps + t Pd – Ps = t 300 – Q = 2Q + t Q* = 100 – t/3 Tax Revenue = t.Q = 100t – t2 / 3 For maximizing tax revenue, 100 – 2t/3 = 0 So, t = 150 Q* = 100 – 50 = 50 Once you get that quantity, you can get DWL (area of triangle) But for that you also need to know the optimal quantity without tax. Equating demand and supply functions, 300 – P = P/2 P = 200 Which implies, Q = 100 DWL = ½ * 150* (100-50) = 3750
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