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 cost
Production — 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
Production -Monopoly Mark-up Pricing Marginal revenue can be written in terms of elasticity. n. The equilibrium condition becomes: MR=ply MC Inl= oo the demand curve is fat and MC=p-the perfectly competitive case. If ml l and MR<O. The monopolist would produce nothing when demand is inelastic The condition MR=MC can be rewritten to give the price mark-up Mark-up=1-1/Inl The mark-up is the factor by which market price exceeds marginal cost. uction- Monopoly Inefficiency: Monopoly vs Competition A monopoly prices higher than a perfectly competitive market. They produce less. Is this efficient? y Recall the demand curve is the "willingness to pay"of the consumers. Suppose a small amount beyond the monopolist's output(ym)was produced. The consumers would pay p(ym + Ay) for this. This exceeds MC Hence there is a positive gain from this extra sale. It would be better for both consumer and monopolist The monopolist refuses to do this however, as a lower price will reduce total profits. A perfectly competitive firm prices at Pe= AC- no gains from further output can be made- it is efficient
Production — Monopoly 3 Mark-up Pricing • Marginal revenue can be written in terms of elasticity, η. The equilibrium condition becomes: MR = p(y) ½ 1 − 1 |η| ¾ = MC • If |η| = ∞ the demand curve is flat and MC = p — the perfectly competitive case. • If |η| 1 and MR < 0. The monopolist would produce nothing when demand is inelastic. • The condition MR = MC can be rewritten to give the price mark-up. p(y) = MC(y) 1 − 1/ |η| =⇒ Mark-up = 1 1 − 1/ |η| • The mark-up is the factor by which market price exceeds marginal cost. Production — Monopoly 4 Inefficiency: Monopoly vs Competition • A monopoly prices higher than a perfectly competitive market. They produce less. Is this efficient? ............................ ................................................................................................................................................................................................................................................................................ . ............ ............. ............. ............. . . . . . ............. ............. ............. ............. ............. . . . . . 0 p y pm ym pc yc p(y) • Recall the demand curve is the “willingness to pay” of the consumers. Suppose a small amount beyond the monopolist’s output (ym) was produced. The consumers would pay p(ym + ∆y) for this. This exceeds MC. • Hence there is a positive gain from this extra sale. It would be better for both consumer and monopolist. • The monopolist refuses to do this however, as a lower price will reduce total profits. • A perfectly competitive firm prices at pc = MC — no gains from further output can be made — it is efficient
Production -Monopoly Deadweight Loss The deadweight loss of a monopoly is a measure of this inefficiency. It is the sum of lost consumer and producer surplus due to the of output and rise in price ply) a+b is the loss in consumer surplus. But a is regained in profit by the firm. It is redistributed, but not lost. c is the loss in producer surplus. Hence total deadweight loss is the area b+c. uction- Monopoly Natural Monopolies The government may wish to force a monopolist to price at marginal cost However, if there are very large fixed costs p=AC may result in negative profits-the firm will close down. This is the case with natural monopolies. The utilities are good examples. ply) In order to allow the firm to cover their costs the government might regulate to set Pa AC. The firm will not wish to close down, but will produce less than an efficient amount at too high a price
Production — Monopoly 5 Deadweight Loss • The deadweight loss of a monopoly is a measure of this inefficiency. • It is the sum of lost consumer and producer surplus due to the restriction of output and rise in price. ............................ ................................................................................................................................................................................................................................................................................ . . ............................................................................................................................. ....................................................................................... . . . 0 p y p ∗ y ∗ pc p(y) a b c • a + b is the loss in consumer surplus. But a is regained in profit by the firm. It is redistributed, but not lost. • c is the loss in producer surplus. Hence total deadweight loss is the area b + c. Production — Monopoly 6 Natural Monopolies • The government may wish to force a monopolist to price at marginal cost. • However, if there are very large fixed costs p = MC may result in negative profits — the firm will close down. • This is the case with natural monopolies. The utilities are good examples. .................. . ...... ............................ ................................................................................................................................................................................................................................................................................ . . . . . ............. ............. ............. ............. ............. ............. ............. ............. . . . . . . 0 p y MC AC pc yc p(y) pa Loss • In order to allow the firm to cover their costs the government might regulate to set pa = AC. The firm will not wish to close down, but will produce less than an efficient amount at too high a price
Production -Monopoly The Minimum Efficient Scale The minimum efficient scale (MES) is the point at which average costs are If this is small relative to demand, there is "room"for many firms charging P* relative to demand. there is"room"for only one firm charging p The MES helps to determine which sort of industry monopolistic or competitive - is likely to arise This makes sense. High fixed costs relative to demand lead to a high MES and make monopoly more likely. Other factors influencing market structure are- the law. historical accident and cartels uction- Monopoly 1st Degree Price Discrimination Suppose the monopolist can sell different units of output at different prices and can sell at different prices to different people. This is Ist degree price discrimination. Each unit will be sold to the person who values it most highly at the maximum price they are willing to pay The demand curve represents consumers willingness to pay. The first unit is sold at the highest price and so on. MC Suppose there are two consumers. The monopolist charges a total of a to the first and the b to the second for consumption of ye and y2 respectively. All the consumer surplus is appropriated by the firm. An efficient amount is produced -output is set where p(y)=MC
Production — Monopoly 7 The Minimum Efficient Scale • The minimum efficient scale (MES) is the point at which average costs are minimised. • If this is small relative to demand, there is “room” for many firms charging p ∗ . • If it is large relative to demand, there is “room” for only one firm charging p ∗ . ............ . ......... ..................................................................................................................................................................................... ................................................................................................................................................................................................................................................................................ .................................................................................................................................................................................................................................................................................. . . ............. ............. .............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. . . . . . . . 0 p y 0 p y AC AC p(y) p(y) p ∗ p ∗ MES MES • The MES helps to determine which sort of industry — monopolistic or competitive — is likely to arise. • This makes sense. High fixed costs relative to demand lead to a high MES and make monopoly more likely. • Other factors influencing market structure are — the law, historical accident and cartels. Production — Monopoly 8 1st Degree Price Discrimination • Suppose the monopolist can sell different units of output at different prices and can sell at different prices to different people. This is 1st degree price discrimination. • Each unit will be sold to the person who values it most highly at the maximum price they are willing to pay. • The demand curve represents consumers’ willingness to pay. The first unit is sold at the highest price and so on. ................................................................................................................................................................................................................................................................................ . .................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................................................ . .. .................................................................................................................................................................................................................................................... . . . . . . . 0 p y MC y 1 c p(y) 0 p y MC y 2 c p(y) a b • Suppose there are two consumers. The monopolist charges a total of a to the first and the b to the second for consumption of y 1 c and y 2 c respectively. All the consumer surplus is appropriated by the firm. • An efficient amount is produced — output is set where p(y) = MC
Suppose a monopolist can sell different units of output for different prices. This is 2nd degree price discrimination often called non-linear pricing. Bulk buying is an example. Suppose MC=0 and two for simplicity. The monopolist would like to lst degree price discriminate. However, it can't. The consumers would lie about their type- the high-willingness-to-pay consumer would pretend to be a low-willingness-to-pay person and pay the lower price. How should the monopolist behave in such scenarios? p2(y) actly what they would get at y Monopolist can do better by decreasing yl. Loses some a. gains some c. Second graph: Monopolist lowers y until marginal gains are exhausted. Sells y at price a and y at price +c+d High type buys y gets uction- Monopoly 3rd Degree Price Discrimin Suppose the firm can sell to different consumers at different prices. This is 3rd degree price discrimination. One consumer(a student)has demand elasticity n and the other(a lecturer)has elasticity n The firm maximises profit: max, - p(y)y+p(y")y-c(y +y)). At the optimum MR(y C(y+y)=MRL Recall marginal written as a function of elasticities- at the optimum Students have more elastic demand so [7>17 This implies that, at the optimum, p(y)<ply) The higher elasticity market faces a lower price. Student cards will obtain a lower price in many shops
Production — Monopoly 9 2nd Degree Price Discrimination • Suppose a monopolist can sell different units of output for different prices. This is 2nd degree price discrimination — often called non-linear pricing. Bulk buying is an example. • Suppose MC = 0 and two consumers for simplicity. The monopolist would like to 1st degree price discriminate. • However, it can’t. The consumers would lie about their type — the high-willingness-to-pay consumer would pretend to be a low-willingness-to-pay person and pay the lower price. How should the monopolist behave in such scenarios? ................................................................................................................................................................................................................................................................................ . . ................................................................................................................................................................................................................................................................................ . . . . . . . . . . . . . 0 p y y L y H p H(y) p L(y) 0 p y y L y H a b c a b c d • First graph: Monopolist sells y L at price a and y H at price a + b + c. High type lies about their type, buys y L and gets b surplus, rather than 0. Could charge a for y L and a + c for y H — now high type self selects y H, gets surplus b — exactly what they would get at y L. Monopolist can do better by decreasing y L. Loses some a, gains some c. • Second graph: Monopolist lowers y L until marginal gains are exhausted. Sells y L at price a and y H at price a + c + d. High type buys y H, gets b, low type buys y L and gets zero surplus. Production — Monopoly 10 3rd Degree Price Discrimination • Suppose the firm can sell to different consumers at different prices. This is 3rd degree price discrimination. • One consumer (a student) has demand elasticity η S and the other (a lecturer) has elasticity η L. • The firm maximises profit: maxyS ,yL © p(y S)y S + p(y L)y L − c(y S + y L) ª . At the optimum: MR S (y S ) = MC(y S + y L ) = MR L (y L ) • Recall marginal revenue can be written as a function of elasticities — at the optimum: p(y S ) ½ 1 − 1 |η S| ¾ = p(y L ) ½ 1 − 1 |η L| ¾ • Students have more elastic demand so ¯ ¯η S ¯ ¯ > ¯ ¯η L ¯ ¯ . This implies that, at the optimum, p(y S) < p(y L). • The higher elasticity market faces a lower price. Student cards will obtain a lower price in many shops
Production -Monopoly Monopoly and Factor Demands The monopolists demand for the factors of production will differ from the perfectly competitive case. en producing output y. The marginal product of the factor is MP,= Ay/Ar, the increase in output due to an increase in the input. The marginal revenue pro res the increase in revenue due to an increase in the input -it is the increase in evenue due to output changes times the increase in output due to increased factor use: MRP:= MR x Ay/Ar The marginal cost of hiring a factor is the price of the input u. A monopolist will demand the factor until the marginal benefit from doing so(MRP) equates to the marginal cost Recall that perfectly competitive firms in equilibrium hired until pAP,= w. The monopolist does not- they only hire until MRPa=w. They employ less of the factor. uction- Monopoly monopsony is a single buyer in a factor marke Suppose the monopsonist sells to a competitive market (this can be easily generalised). The firm will maximise profit: max pf(r)-wfr)r. (f(r)is the production function The firm will operate where pMP,= MCr. But the marginal cost is no longer a constant w. The firm faces the ve(much like a monopolist faces the entire demand curve). Marginal costs written as MC = u(r)(1+1/ns)where ns >0 is the price elasticity of supply. Hence marginal costs lie to the left of the supply curve. The firm will hire rat price u" They demand less, and pay a lower price for it than a competitive firm- inefficient. Minimum wage?
Production — Monopoly 11 Monopoly and Factor Demands • The monopolist’s demand for the factors of production will differ from the perfectly competitive case. • Suppose there is only one factor of production, and the monopolist demands x of it when producing output y. • The marginal product of the factor is MPx = ∆y/∆x, the increase in output due to an increase in the input. The marginal revenue product measures the increase in revenue due to an increase in the input — it is the increase in revenue due to output changes times the increase in output due to increased factor use: MRPx = MR × ∆y/∆x. MRPx = p(y) ½ 1 − 1 |η| ¾ MPx ≤ p(y)MPx • The marginal cost of hiring a factor is the price of the input w. A monopolist will demand the factor until the marginal benefit from doing so (MRPx) equates to the marginal cost. • Recall that perfectly competitive firms in equilibrium hired until pMPx = w. The monopolist does not — they only hire until MRPx = w. They employ less of the factor. Production — Monopoly 12 Monopsony • A monopoly is a single seller in a market. A monopsony is a single buyer in a factor market. • Suppose the monopsonist sells to a competitive market (this can be easily generalised). • The firm will maximise profit: maxx {pf(x) − w(x)x}. (f(x) is the production function). • The firm will operate where pMPx = MCx. But the marginal cost is no longer a constant, w. The firm faces the entire supply curve (much like a monopolist faces the entire demand curve). ................................................................................................................................................................................................................................................................................ .............................................................................................................................................................................. . . ............. ............. ............. .......... . . . . . . . .......... ............. ............. ............. 0 w x MCx Supply MR = pMPx MR = MC w ∗ x ∗ • Marginal costs can be written as MCx = w(x)(1 + 1/ηS) where ηS > 0 is the price elasticity of supply. Hence marginal costs lie to the left of the supply curve. The firm will hire x ∗ at price w ∗ . • They demand less, and pay a lower price for it than a competitive firm — inefficient. Minimum wage?
