Production -Monopoly Profit Maximisation The monopolist is the only firm in the industry. Therefore, they face the entire demand curve. Profits are given by total inus total costs. x=p(y)y-c(y). ply) is the inverse demand curve. The monopolist is assumed to maximise profits. That is. they choose output to solve: maxT= max p(y)y-c(y) MREMC he maximisation condition is m ost, and if MR< MC a decrease in output would generate more revenue than cost As there are barriers to entry. no firm can enter if positive profits are being made and the short run is the san the long run. A monopolist can earn positive profits in the long run- unlike competitive firms. uction- Monopoly The Monopoli These facts can be illustrated in the following essential diagram. MC AC AR=py Note that revenue is p(y)y. So average revenue is AR= ply)y/y= py), which is the inverse demand curve. AR falls at twice the rate of AR for linear demand. MC= MR generates the optimal quantity y. To find the optimal price(p")use the demand curve value at y. Finally, profits are given by i (the box with a dashed outline), the area between average revenue and average costProduction — Monopoly 1 Profit Maximisation • The monopolist is the only firm in the industry. Therefore, they face the entire demand curve. • Profits are given by total revenue minus total costs. π = p(y)y − c(y). p(y) is the inverse demand curve. • The monopolist is assumed to maximise profits. That is, they choose output to solve: max y π = max y p(y)y − c(y) =⇒ MR = MC • The maximisation condition is MR = MC. If MR > MC then an increase in output generates more revenue than cost, and if MR < MC a decrease in output would generate more revenue than cost. • As there are barriers to entry, no firm can enter if positive profits are being made and the short run is the same as the long run. A monopolist can earn positive profits in the long run — unlike competitive firms. Production — Monopoly 2 The Monopolist • These facts can be illustrated in the following essential diagram. .................. ...... ............................ ................................................................................................................................................................................................................................................................................ . . . . . . . . . . . . ............ ............. ............. ............. ............ ............. ............. ............. 0 p y MC AC p ∗ y ∗ AR = p(y) MR π • Note that revenue is p(y)y. So average revenue is AR = p(y)y/y = p(y), which is the inverse demand curve. • MR falls at twice the rate of AR for linear demand. MC = MR generates the optimal quantity y ∗ . • To find the optimal price (p ∗ ) use the demand curve value at y ∗ . Finally, profits are given by π (the box with a dashed outline), the area between average revenue and average cost