A monopolist faces an inverted market demand curve given by P(

A monopolist maximises profit at the output where MR = MC. We find this output before and after the tax and compare the two prices. Before the tax: TR = P × Q = (200 - 4Q)Q = 200Q - 4Q² MR = d(TR)/dQ = 200 - 8Q MC = d(TC)/dQ = 4Q + 20 (the fixed cost of 100 vanishes on differentiation) Setting MR = MC: 200 - 8Q = 4Q + 20, so 12Q = 180 and Q = 15. P = 200 - 4(15) = ₹140. After the tax: A specific tax of ₹12 per unit raises the cost of every unit by ₹12, so TC becomes 2Q² + 32Q + 100 and MC = 4Q + 32. The demand curve does not change, so MR remains 200 - 8Q. Setting MR = MC: 200 - 8Q = 4Q + 32, so 12Q = 168 and Q = 14. P = 200 - 4(14) = ₹144. Change in price = 144 - 140 = ₹4. Only one-third of the tax (₹4 out of ₹12) is passed on to consumers. The monopolist bears the remaining ₹8, because raising the price by the full ₹12 would cost him too many sales. Quick method: for demand P = a - bQ and MC = c + dQ, the price rise due to a per-unit tax t is bt/(2b + d) = (4 × 12)/(8 + 4) = ₹4. Hence the correct option is (B).