Price can be written as P = 155 - Q. (A) TR is price multiplied by quantity for TR = P × Q = 155 × Q - (0.25) × Q 2 . Marginal revenue is MR = 155 - 2 × Q d . Marginal costs are MC = 110 - 0.5 × Q. MC = MB for monopolist Q* = 30, P* = 125, TR = P × Q = 125 × 30 = 3,750 Profits = TR - TC = 3,750 - [110 × 30 - (0.25) 30 2 ] = 675. (B) AC = TC/Q = 110 + (0.25) × Q. AC = D if the government intervenes, 110 - (0.25) × Q = 155 - Q so Q* = 60 and P* = 95 TR = P × Q = 60 × 95 = 5,700 Profits = TR - TC = 5,700 - [110 × 60 - (0.25) × 60 2 ] = 0 (C) Now the monopolist produces at perfectly competitive market quantity, S = D so MC = D thus 110 + (0.5) × Q = 155 - Q Q* = 90 and P* = 65 TR = P × Q = 65 × 90 = 5,850 Profits = TR - TC = 5,850 - [110 × 90 - (0.25) × 90 2 ] = - 2,025
(A) If the original price of the good was $10 and a $4 tax was imposed, what is the tax
income? What is the excess burden?
(B) How much marginal excess burden will be created if an additional dollar of tax is levied?
(C) How much additional tax is collected?
(A) If the original price of the good was $10 and a $4 tax was imposed, tax income is the
shaded area denoted by abhj. Q* with no tax can be calculated as 10 = 50 - 2Q and Q* = 20. If
$4 of tax is levied, then Q 1 = 18, then the Tax = (14 - 10) × (18) = $72, excess burden is the
shaded area denoted by abc which is equal to 4 * 2/2 = $4
(B) If an additional tax is levied then Tax = $5, P = 15, Q 2 = 17.5. Marginal excess burden is
the shaded area denoted by fbae which is equal to [(1/2) * (1/2) * 1 + (1/2) * 4] = $2.25
(C) Additional tax is collected is the difference between shaded area denoted by gfih and baei
which is equal to [(1 * 17.5) - (4 * 1/2)] = 15.5
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