Monopoly vs. Compe22on. Theory of the Firm. Causes of Monopoly. Monopoly vs. Compe22on. Monopolis2c Markets P. Natural. Legal.

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1 Monooly vs. Comeon Monooly Perfect Come,,on Theory of the Firm P Monooly s demand = Market demand (ΔQ P) P Firm s demand = Horizontal line ( Δ P does not change) Monoolisc Markets P d Q Monooly vs. Comeon Causes of Monooly Monooly One firm (market ower) Barriers to entry Perfect Come,,on Many rice-taking firms Free entry/exit Natural 1. Scarcity of a resource: one firm owns a key resource (e Beers iamonds). Technological reasons: existence of large economies of scale relave to the market size -- one firm may serve the demand more efficiently than several firms (water, telehone, ) Legal 1. Licenses (taxis, harmacies, notaries, ). Patents (medical drugs, intellectual roerty, )

2 P Natural Monooly A natural monooly arises when there a large economies of scale: cost minimizaon would lead to a single firm roducing the total outut. First Order Condion: Profit Maximizaon π'() = 0 () = (). P M Second Order Condion: '( ) + ''( ) '( ) 0 Q M Q Shutdown Condion: π( M ) π(0) The Monoolist s Problem The revenue funcon of the monooly is R() = (), where () is the INVERSE demand funcon. C,R, π Profit Maximizaon C() R() Sloe = Therefore the roblem of the monoolisc firm is Max 0 π() = () C(). Sloe = π() M

3 Profit Maximizaon: Marginal revenue is given by d ( ) = d (+) ( ) ( ( ) ) = ( ) + '( ). Profit Maximizaon: Marginal Revenue: () = () + (). The two terms in this exression have a very clear interretaon: the sale of one addional (infinitesimal) unit generates (a) an increase of revenue eual to the rice (uanty effect), and (b) a decrease of revenue eual to the total outut mes the reducon in rice necessary to generate the demand of this addional unit (rice effect). () (Since () < 0, the curve is always below the demand curve.) P() Profit Maximizaon: Profit Maximizaon: SOC P The Second Orden Condion is: A: uanty effect B: rice effect '( ) + ''( ) ' 0 B A = A B. P() Since () < 0, the condion C () > 0 (reuiring that the firm has diseconomies of scale near the omal level of outut) is no longer reuired for rofit maximizaon: at the omal roducon level the firm may have economies of scale. +1

4 Monooly Euilibrium Surlus and Profits Monooly Perfect Comeon M CS PS WL C CS PS M C CS π = PS M WL C = M C Monooly Euilibrium In a monooly, the rice is above the comeve rice, M > C, Lerner Index First Order Condion for rofit maximizaon is: the outut is below the comeve outut, M < C, the consumer (roducer) surlus is below (above) the comeve surlus CS M < CS C (PS M > PS C ), Marginal revenue is () = (). and the total surlus is below the comeve surlus, TS M < TS C. ( ) = + '( ) = + '( ). Also, there is a eadweight Loss, WL = TS C -TS M > 0.

5 Lerner Index We can write the monooly rice as a funcon of the demand rice-elascity. The demand rice-elascity is Lerner Index The Lerner index measures monooly ower: it exlains the ercentage of rice that is not due to costs. Then, ε = '() = '(). = 1+ 1 =. ε It is defined as L = M ( M ) M = 1 ε. Note that 0 L 1. (L = 0 under erfect comeon.) Lerner Index Examle If demand is very elasc (Ɛ high), the margin will be small; and vice versa: A monoolist faces the demand funcon () = max{1, 0}, and its cost funcon is C() = 5+4. M ( M ) M ( M ) We calculate the monooly euilibrium, the consumer and roducer surluses and the deadweight loss, the monooly rofits, the Lerner index. M M

6 Examle Monooly Euilibrium. Revenue is R() = (1 ) = 1. Hence () = 1. Examle We calculate the Lerner index: LI = ( M ( M ))/ M = (8-4)/8 = Since () = 4, the euilibrium outut is given by the euaon () = () 1 = 4. Thus, M = 4, and M = 1 M = 1 4 = CS PS Monooly WL Perfect Comeon Examle We calculates the consumer and roducer surlus and the monooly s rofit: CS = 0.5*(1 M )* M = 0.5*(1-8)*4 = 8; PS = ( M CMa)* M = (8-4)*4 = 16; π() = M M C( M ) = 8*4 (5 + 4*4) = 11; Since the comeve euilibrium is C = 4, C = 8, we have: WL = 0.5*( M C )( C M ) = 0.5*4*4 = 8. Regulang a Monooly An unregulated monooly generates a deadweight loss, WL>0. Can this be avoided? An obvious soluon (if ossible that is, if we know the monooly s cost funcon), is to imose a regulated rice eual to marginal cost, thus generang the comeve outcome. This soluon may lead to monooly s losses that would have to be subsidized. When subsidizing is not ossible or convenient (rising the necessary revenue may involve other inefficiencies), an alternave regulated rice may be the average cost.

7 Regulang a Monooly Taxes P = () In a monooly, as in a comeve market, introducing a tax causes an increase in rices and a decrease in outut, and therefore, a deadweight loss. Subsidy = C *(( C ) C ) The rooron of the tax that is aid for by consumers deends, in a monooly as well as in a comeve market, of the rice elascity of the demand. ( C ) C C Regulang a Monooly Price Cas P = () Recall that in a comeve market introducing a rice ca (i.e., a maximum rice at which the good may be traded), reduces the level of outut (and creates an excess demand that reuires raoning the demand), results in a deadweight loss (reduces the total surlus) and may or may not increase the consumer surlus. R eadweith loss In a monooly, however, introducing a rice ca below the euilibrium rice may be an effecve instrument to decrease the rice and increase the outut. Moreover, if the rice ca is above marginal cost, then it does not create an excess demand, and results in a greater consumer and total surlus, and smaller deadweight loss. C R C

8 Taxes and Price Ca: an Examle Monooly:Taxes Consider a monoolist whose cost funcon is C() = 5+4 facing the demand () = max{1, 0}. The monooly outut is the soluon to the euaon 1- = 4 Therefore M = 4, and M = 8. C M S 1 11 T 1. Suose we introduce a tax T=1 /unit. 4 emand: (,T)=max{1 (+T), 0}. Revenue: R(,T) = (1 T) = 1 T. Marginal Revenue: () = 1 T. (,T) () T M Monooly: Taxes The euaon () = () is now 1 T = 4 Hence outut is M (T) = 4 T/, the consumer rice is M (T) = 8 + T/, and monooly rice = 8 + T/ T = 8 T/. That is, the tax burden is shared eually between the consumers and the monooly. Monooly: Taxes () = () 1 T = 4 (T) = 4 T/. With the taxe T, the rice aid by the consumer and the rice received by monooly are not the same: Price aid by consumer = 1 (T) = 8 + T/ Price received by monooly = 8 + T/ T = 8 T/. In this case, the tax burden is shared eually between the consumers and the monooly.

9 Taxes and Price Ca: an Examle. Suose we introduce a rice ca + < 8 = M. The rice ca changes de revenue funcon of the monooly 1 if 1 - R( + +,) = + if 1 > + The Marginal Revenue is: 1 if 1 - ( + +,) = + if 1 > + Para + = 7, the euilibrium is = 5 and = + =7 (see the grah in the age). Price iscriminaon So far, we have assumed that the monooly charges the same rice for each unit. We now discuss how the monooly may increase its rofit by charging different rices to different consumers with different WILLINGNESS TO PAY. Monooly:Taxes Price iscriminaon C 1 11 M =8 + =7 First degree: the monooly sells each infinitesimal unit at the maximum rice a consumer is willing to ay. With this ricing olicy we obtain CS=0, PS = TS = maximum surlus, WL=0. 4 M =4 +=5 + () Second degree: The monooly uses NON-LINEAR ricing olicies: for examle, volume discounts. This tye of discriminaon is very common in water, electricity, telehone and internet sulies.

10 Third egree Price iscriminaon The monooly tries to segment the market (by geograhical criteria, by customers features, etc.), and charges different rices to each market segment. Examle: There are two grous of consumers, 1 and, whose demands are 1 ( 1 ) and ( ). Third egree Price iscriminaon The monoolist chooses 1 and to maximize the total rofits: π( 1, ) = R 1 ( 1 ) + R ( ) C ( 1 + ) = 1 ( 1 ) 1 + ( ) C( 1 + ) FOC: ( ) = ( 1 1 ( 1 ) = ( ) ). Third egree Price iscriminaon Ɛ > Ɛ 1 Grou 1 Grou 1 1 Third egree iscriminaon In terms of elascies: 1 (1+1/Ɛ 1 ) = (1+1/Ɛ ) = ( 1 + ) Therefore 1 / = (1+1/Ɛ )/(1+1/Ɛ 1 ) < 1; and 1 < ; 1 1 That is, monooly rice is lower in the market with a more elasc demand.

11 Suose a monooly roduces a good with costs C() = /, and faces two markets with demands and Third egree Price iscriminaon: Examle 1 ( 1 ) = max{0 1,0} ( ) = max{60,0}. etermine the uanes, rices and total rofits under third degree rice discriminaon, and without rice discriminaon. Third egree Price iscriminaon: Examle (b) Without rice discriminaon: the aggregate demand is 80 3 ( ) = if 0 3 if 0 < 30 ( ) = 30 > if 30 0 Monooly euilibrium: () = () Solving, we obtain M = 15, M =.5. Monooly rofits are: π = if 0 if < 0 if > Third egree Price iscriminaon: Examle (a) Third degree discriminaon: ( 1 + ) = 1 + R 1 = = 0 1 R = * = 30 Euilibrium: 0 1 = 30 = 1 + Solving, we obtain 1 =, = 14, 1 = 18 and = 3. Monooly rofits are π = 18* + 14*3 C(+14) = 30.

c 2009 Je rey A. Miron 3. Examples: Linear Demand Curves and Monopoly

c 2009 Je rey A. Miron 3. Examples: Linear Demand Curves and Monopoly Lecture 0: Monooly. c 009 Je rey A. Miron Outline. Introduction. Maximizing Pro ts. Examles: Linear Demand Curves and Monooly. The Ine ciency of Monooly. The Deadweight Loss of Monooly. Price Discrimination.