Given:

• General market demand function P(Q)
• Constant MC

Find:

• DWL generated by a uniform-pricing monopolist can be approximated by half of monopoly profits

Is this approach correct? Is there another way? How would you approach this?

My approach:

• Let c = constant cost
• Total Revenue = (P * Q)
• Marginal Revenue (MR) = d(TR) / d(Q)
• Monopolist produces at the Q where MR = MC, in other words: MR = c
• Find Q where MR = c , call monopoly Quantity Q_m
• Monopoly price P_m = P_m(Q_m)
• Monopoly Profit pi = Total Revenue - Total Cost = ( P_m * Q_m ) - ( c * Q ) = Q_m (P_m - c) or pi = (P_m - MR(Q_m)) ( Q_m)
• Find competitive equilibrium Q_c and P_c. Q_c is where P = MC. Use Q_c to find P_c.
• DWL = 1/2 * (P_m - P_c) * (Q_c - Q_m)
• Compare pi and DWL ?

Is my approach correct here? Can you show me your approach?