Imperfect Competition 4/26/2017 Imperfect Competition 1-Pure Monopoly 2-Monopolistic competition 3-Oligopoly MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Pure Monopoly There is only on seller in the market Market demand curve is downward sloping She can either change price or quantity in order to maximize the profit In order to sell more , she should lower the price She is facing the market demand individually MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Monopoly demand Q = F(p) or P = F (q) Unique inverse P b P a P 1 Q1 Q Q MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Average and marginal revenue imperfect competition 4/26/2017 Average and marginal revenue R=p(q)q total revenue MR=dR/dq=p+q(dp/dq)=p(1+(q/p)(dp/dq))= p(1-1/ e ) e=absolute value of elasticity dp/dq<0 MR<P p=a-bq then q=(p-a)/b TR = aq- bq2 , then MR = a – 2bq q = (a-MR)/2b p= a-bq q=(a-p)/b p D MR q P=MR ; q(Demand)= 2q(MR) MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MR=P(1- 1/ιeι ) If Q=Q* , ιeι=1 , MR=0 , R(Q)=MAX If Q<Q* , ιeι>1 , MR>0 , If Q>Q* , ιeι<1 MR<0 , P Monopolist will always produce in the elastic portion of the demand curve MR P * D = AR Q* Q MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 e=1 Demand, Total Revenue and Elasticity Demand, Total Revenue and Elasticity Demand, Total Revenue and Elasticity e<1 demand Max TR TR elasticity MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Profit maximization cost function imperfect competition 4/26/2017 Profit maximization cost function П=p(Q)Q – C(Q) = TR(Q) – TC(Q) dП/dQ = dTR(Q)/d(Q) – dTC(Q)/Q = 0 MR(Q) = MC(Q) F.O.C. MR>0 , Monopolist always choose a point on the elastic portion of the demnad. dMR(Q)/dQ < dMC(Q)/dQ S.O.C. MC must cut MR from below If first and second order condition satisfies for More than a point , the one which yield greater profit will be chosen. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Figure 1 and 2 satisfies the S.O.C. but 3 does not MC MC p p p MR D D MR D MR MC q q q MICROECONOMICS 1 IMPERFECT COMPETITION 2 1 3 MICROECONOMICS 1

Profit maximization : production function imperfect competition 4/26/2017 Profit maximization : production function П=TR(q) - r1x1 – r2x2 Q= h(x1,x2) dП/dxi = MR(q)hi – ri = 0 MR(q)hi = ri MRPxi= ri MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 VMPxi = ri F.O.C. S.O.C. П11<0 , П22<0 , П11П22 – П212>0 Пii = MR(q)hii + dMR(q)/dq hi2<0 MR’(q)<-MR(q)hii/hi2=-rihii/hi3 MC=ri/hi MC=MR MR‘ (q ) is negative for monopolist . So hii could be positive ( MPxi is increasing) and monopolist may produce where production function is not concave .(the condition for concavity requires hii to be negative ). MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Price discrimination Selling at more than one price to increase profit Buyers should be unable to buy from one market and sell it in other one Personal services ; electricity , gas, water Saptially seperated markets, domestic and export markets MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Price discrimination П=R1(q1)+R2(q2)-C(q1+q2) qi= Sale in the ith market Ri(qi) = piqi revenue in the ith market dП/dqi=MR(qi)-MC(q1+q2) = 0 i=1,2 MR(q1)=MR(q2)=MC(q1+q2) P1(1-1/e1)=P2(1-1/e2) Greater elasticity lower price S.O.C. dП/dqi <0 dMRi(qi)/dq<dMC(q)dq i=1,2 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Perfectly discriminating monopolist imperfect competition 4/26/2017 Perfectly discriminating monopolist The monopolist is able to subdivide her market to such a degree that she could sell each successive unit of her commodities for the maximum amount that consumers are willing to pay. The consumers should have different elasticity's of demand for the monopolist output. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 П = F(Q) - MC(Q) dП/dQ=0 F(Q) – MC(Q) = 0 F . O . C . ; Marginal price =Marginal cost S .O . C . ; Slope of demand <Slope of marginal cost P MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Multi plant monopolist imperfect competition Multi plant monopolist 4/26/2017 Output (q) will be produced in two separate plant (i) qi = production in plant i Output of Plants will be sold in a single market. П = R(q1+q2) – C1(q1) – C2(q2) Ci(qi) = cost of production in plant i dП/dq1= MR(q1+q2) – MC(q1) = 0 dΠ/dq2 = MR(q1+q2) – MC(q2) = 0 MC(q1) = MC(q2) = MR(q1+q2) F.O.C. dMC(qi)/dqi>dMR(q1+q2)/dqi S.O.C. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Multi product monopolist imperfect competition 4/26/2017 Multi product monopolist Two distinct product Q1=F1(p1,p2) Q2=F2(p1,p2) P1=f1(q1,q2) p2=f2(q1,q2) R1(q1,q2)=p1q1 R2(q1,q2)=p2q2 Π=R1(q1,q2) + R2(q1,q2) - C1(q1) - C2(q2) dΠ/dq1=dR1/dq1+dR2/dq1 – MC1(q1)=0 dΠ/dq2=dR1/dq2 +dR2/dq2 – MC2(q2)=0 92 9 19 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Multi product monopolist imperfect competition 4/26/2017 Multi product monopolist dR1/dq1+dR2/dq1=MC1(q1) dR1/dq2+dR2/dq2=MC2(q2) If q1 increase by one unit and q1 is a substitute for q2 (dR2/dq1<0) , then Revenue increase by (dR1/dq1+dR2/dq1) Cost increase by MC(q1) For profit maximization these two should be the same for one unit increase in q1 checked MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Monopoly taxation 1- Lump-sum tax Π=R(q)-C(q)-T dΠ/dq=MR(q)-MC(q)=0 MR=MC Same output as before the tax Only monopoly profit will decrease 2-Profit tax 0<t<1 Π=R(q)-C(q)-t{R(q)-C(q)}=(1-t){R(q)-C(q)} dΠ/dq=(1-t){MR(q)-MC(q)}=0 MR=MC 83 11 11 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopoly taxation continued imperfect competition 4/26/2017 Monopoly taxation continued 3- specific sale tax T=αq Π=R(q)-C(q)-αq dΠ/dq=MR(q)-MC(q) -α =0 Profit maximization condition will change dq/dα=1/(dMR(q)/dq-dMC(q)/dq) (dMR(q)-dMC(q))/dq<0 S.O.C. dq/dα<0 Increase in tax rate(α) will lead to decrease in quantity produced and Increase in price MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopoly taxation cont. imperfect competition 4/26/2017 Monopoly taxation cont. T = sR(q) 0<s<1 Π=R(q)-C(q)-sR(q)=(1-s)R(q)-C(q) dΠ/dq=(1-s)MR(q)-MC(q)=0 (1-s)MR(q)=MC(q) Taking total differential dq/ds=MR(q)/{(1-s)(MR’(q)-MC’(q)} <0 By S.O.C. < 0 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Revenue maximizing monopoly imperfect competition 4/26/2017 Revenue maximizing monopoly Max R(q) s.t. Π=R(q)-C(q) ≥Π0 L= R(q) +λ{R(q) - C(q) – Π0} dL/dq = MR(q) + λ {MR(q)-MC(q)} ≤ 0, q dL/dq=0 dL/dλ=R(q) - C(q) – Π0 ≥ 0 , , λdL/dλ= 0 If Π0 =Π* =maxΠ then MR(q) – MC(q) = 0 q=q* If Π0> Π* no solution 15 11 90 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 TC Profit when revenue is maximized TR is max C , TR MR=MC TR max Π = Π* q=q* MR>0 MC>0 q* q qm (TR is max) MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Revenue maximizing cont. imperfect competition 4/26/2017 Revenue maximizing cont. If Π0<Π* then Π should be greater than or equal to Π0 , 1-When Π0 is less than profit at q=qm(when TR is maximized) , the solution is where TR is maximized [ MR =0 (q=qm)] dL/dq=MR(q)+λ{MR(q)-MC(q)} ≤ 0 If MR =0 so maximized TR is the solution, so there is no constraint., so λ=0 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Revenue maximizing cont. imperfect competition Revenue maximizing cont. 4/26/2017 2- if Π is greater than the profit where q=qm(TR is max) and is less than the maximum profit ,the solution for q is when q*<q<qm . Profit tax will alter the output of revenue maximizing monopoly ; Max R(q) s.t. (1-t){R(q)-C(q)}=Π0 Taking total differential ; dq/dt= {R(q)-C(q)}/(1-t){MR(q)-MC(q)}<0 By S.O.C MR<M.C MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Inefficiency of Monopoly: MC(y*+1) < p(y*+1), so both seller and buyer could gain if (y*+1) level of output is produced. Market is Pareto inefficient $/output unit p(y) CS p(y*) MC(y) PS y* y MICROECONOMICS 1 IMPERFECT COMPETITION MR(y) MICROECONOMICS 1

imperfect competition 4/26/2017 Inefficiency of Monopoly: DWL = gains from trade not achieved $/output unit p(y) p(y*) MC(y) DWL y* MR(y) y MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Inefficiency of Monopoly Inefficiently low quantity, inefficiently high price $/output unit p(y) p(y*) 85 11 13 MC(y) DWL p(ye) y* ye y MICROECONOMICS 1 IMPERFECT COMPETITION MR(y) MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Inefficiency resulting from two-price monopoly is lower than one-price monopoly Z<W The Efficiency Losses from Single-Price and Two-Price Monopoly Efficiency loss Z < W MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Welfare loss from monopoly pricing; Comparing to perfect competition wThe Welfare Loss from a Single-Price Monopoly Loss = (Π+s1+s2)–s2 Monopoly profit 84 11 25 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 87 11 19 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Monopsony The sole purchaser in the market Producer of q is the sole purchaser in the labor market and sell her output in the competitive market. q=h(x) q=output x=input r=price of x , r=g(x) , g’>0 R(q)=pq TC= rx = x g(x) Marginal cost of labor = d(TC)/dx= g(x) +xg’(x) 86 11 16 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 monopsony Π=TR – TC= ph(x) – g(x)x dΠ/dx=ph’(x) – g(x) – xg’(x)=0 Ph’(x)= g(x) +xg’(x) F.O.C. VMPx=MCx(marginal factor cost) d2Π/dx2=ph’’(x) – 2g’(x) – xg’’(x)<0 S.O.C. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MCx=dc/dx C g(x)=supply x r1 r0 VMPx x0 x1 x MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Monopsony If monopsony is a monopolist in the output market , p=F(q) q=h(x) r=g(x) Π=pq – g(x)x =F(q) h(x) – xg(x) dΠ/dx = [ dF(q)/dq ] [ dq/dx ] h(x) + [ dh(x)/dx ] F(q) – [ dg(x)/dx ] x – g(x) =0 [dh(x)/dx ] { [dF(q)/dq] (h(x)] + F(q) } = g(x) + x { dg(x)/dx } checked VMPx MCx MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopolistic competition imperfect competition 4/26/2017 Monopolistic competition Number of sellers is sufficiently large that the actions of an individual seller have no perceptible influence upon her competitors. Each seller has a negatively sloped demand curve for her distinct product . Pk=Ak – akqk – Σi bkiqi i≠k dpk/dqi= - bki <0 i= 1,,,,n 87 11 21 90 11 18 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopolistic competition imperfect competition 4/26/2017 Monopolistic competition If bki=b , ak=a , Ak=A , Ck(qk)=C(qk) Pk = A – aqk – bΣqi i=1…..n Πk=qk(A – aqk – bΣqi) – C(qk) i≠k Representative firm assumes that when she maximizes profit ,the other fellows do not change their output level ,so she can move along her individual demand curve . MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopolistic competition imperfect competition 4/26/2017 Monopolistic competition MR = MC F O C A – 2aqk – b Σqi = MC(qk) i= 1,,,,n dMC/dq>dMR/dq S.O.C. But the other firms will follow the action of the representative firm and do the identical variation The representative firm can not move along her individual demand curve based upon her assumption about the other firms. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopolistic competition imperfect competition 4/26/2017 Monopolistic competition She is forced to move along the effective demand curve , assuming that the others will do the same action ; So replace qk=qi in pk=A - aqk – bΣin qi effective demand for the firm ; Pk=A-[a+(n-1)b]qk which accounts for the simultaneous move of all other firms (steeper slope). MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Monopolistic competition Is a function of qk and n only The Monopolistic Competitor’s Two Demand Curves The Monopolistic Competitor’s Two Demand Curves The Monopolistic Competitor’s Demand Curves The Monopolistic Competitor’s Two Demand Curves The Monopolistic Competitor’s Two Demand Curves The Monopolistic Competitor’s Two Demand Curves The Monopolistic Competitor’s Two Demand Curves Initial position Effective demand curve A function of qk and qi Individual demand curve Change in the quantity is restricted for a firm on the effective demand curve ,because of rival competition. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopolistic competition short run equilibrium imperfect competition 4/26/2017 Monopolistic competition short run equilibrium The industry and an individual firm reaches to an equilibrium when all firms maintain MR=MC pk=A- aqk – bΣin qi MR(q) = A – 2aqk – bΣin qi =MC(qk) one equations and n unknowns (qi) All firms act the same ( qi=qk) A - [2a+(n-1)b]qk=MC(qk) 85 11 15 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 In the short run the number of firms (n) is known ,so the MR=MC equation could be solved for qk as it is shown in the following figure; -Run Equilibrium for the Maximum profit output of the representative firm k when profit is maximized MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopolistic competition Long run equilibrium imperfect competition 4/26/2017 Monopolistic competition Long run equilibrium Positive profit ,free entry , dd shifts to the left ,profit goes back to zero. Π=qk(A – aqk – bΣin qi) – C(qk), qk=qi Πk=Aqk - [a+(n-1)b]qk2 - C(qk) =0 (1) A – 2[a + (n – 1)b]qk = MC(qk) (2) (MR=MC) Two equations two unknown; (n,qk) . MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Monopolistic competition long run equilibrium Long-Run Equilibrium in the Chamberlain Model Monopolistic competition price and quantity Output of the representative Firm k Min LAC Pc c Perfect competition price and quantity Qc MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Oligopoly The result of any move on the part of a oligopolies depend upon the reactions of his rivals. General price-quantity relationship can not be defined, because he can not control the output of other firms. It depends to the assumption which we make about the behavior of his rivals. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Oligopoly If dΠi/dqj is negligible we will have perfect competition or monopolistic competition. If dΠi/dqj is noticeable we will have duopolistic or oligopolist Different assumptions about the behavior of the rivals leads to different models of oligopoly . these assumptions may be as follows ; MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

1- Quasi-competitive solution imperfect competition 4/26/2017 Two firms produce homogenous product q. P=F(q1+q2); Demand function qi = output levels of firm i=1,2 TR1=q1F(q1+q2) TR2=q2F(q1+q2) Π1=TR1(q1,q2) – TC1(q1) Π2=TR2(q1,q2) – TC2(q2) Each follows the competitive solution by equating price to marginal cost , or P=MC, price in the market could be determined in any way. P=F(q1+q2) = MC(q1) P=F(q1+q2) = MC(q2) Two equation two unknowns q1 q2 MICROECONOMICS 1

imperfect competition 4/26/2017 2- Collusion solution All the firms are under a unique control forming a monopoly . P=F(q1+q2) TR1=q1F(q1+q2) TR2=q2F(q1+q2) TR(q1+q2)= Total revenue= TR1+TR2= (q1+q2)F(q1+q2) MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 2-Collusion solution Π=Π1+Π2=TR(q1+q2)-TC1(q1)-TC2(q2) dΠ/dq1 = dTR(q1+q2)/dq1 – MC1(q1)=0 dΠ/dq2 = dTR(q1+q2)/dq2 – MC2(q2)=0 MR(q1+q2)=MC1(q1) MR(q1+q2)=MC2(q2) Two equations two unknowns q1 ,q2 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Cournot solution Homogenous product Classical solution; quantity produced by the rival is invariant with respect to the firm’s output level . P=F(q1+q2) demand curve TRi = qiP = qi F(q1+q2) i= 1,2 Π1=TR1(q1,q2) – TC1(q1) Π2=TR2(q1,q2) – TC2(q2) dTRi /dqi = P+(dp/dq)qi dp/dq <0 q=q1+q2 The firm with greater output will have smaller MR 84 11 30 86 11 21 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Cournot solution dΠ1/dq1=dTR1/dq1–dTC1(q1), MR1=MC1 dΠ2/dq2=dTR2/dq2–dTC2(q2), MR2=MC2 Satisfying the second order coditioin; q1=f1(q2) 1th reaction function q2=f2(q1) 2th reaction function The reaction functions shows for any value of qi(i=1,2), the corresponding value of qj(j=2,1) which maximizes Πj. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Cournot solution q2 q1=f1(q2) Reaction functions q2=f2(q1) q2* q1 q1* MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Cournot solution In some cases the cournot solution coincides with the quasi-competitive P=aqb , q=q1+q2…+qn , Πi = pqi – TCi = aqb qi – TCi dΠi/dqi= d(aqb qi)/dqi - MC =0 , q=nqi , MC=c qi= c1/b/n(b-1)/b(an+ab)1/b If n is infinite then qi=(c/a)1/b P=MC , aqb=c , q=(c/a)1/b MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Cournot solution It is expected to see the following result given the same conditions ; Qcollusion<Qcournot<Qquasi-competitive Pquasi-competitive<Pcournot<Pcollusion Πquasi-competitive<Πcournot<Πcollusion With the appropriate agreement on how to distribute the industry profit, both firms would be better off with collusion comparing to other cases. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Stackelburg solution Π1=h1(q1,q2) Π2=h1(q1,q2) dΠ1/dq1=dh1/dq1+(dh1/dq2)(dq2/dq1) dΠ2/dq2=dh2/dq2+(dh2/dq1)(dq1/dq2) It is rather unrealistic to assume that each firm assumes that his decision do not affect his rival behavior,instead it is more likely that his rival will adjust his behavior according to a reaction function (dqi/dqj) MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Stakelburg solution Assumption about dqi/dqj(leadership follower ship model); A follower obeys his reaction function and adjust his output to maximize his profit , given the quantity decision of his rival whom he assumes to be a leader. A leader does not obey his reaction function , the leader will maximize his profit given the reaction function of his rival whom he assumes to be a follower. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Stackelberg solution Suppose that firm 1 is leader and 2 is follower; Firm 1 assumes that 2’s reaction function (f2(q1)) is valid and substitute 2’s reaction function in his profit function ; Π1=h1[q1,f2(q1)] Then he maximizes his profit function with respect to his output , q1.when q1 is determined, firm 2 will find his output level (q2) from his reaction function , q2=f2(q1) MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Stackelberg solution 1 is leader ,2 is follower , determinate. 2 is leader ,1 is follower , determinate. 1 is follower, 2 is follower, cournot . 1 is leader , 2 is leader , disequilibrium, Most frequent result is the negotiation between the two when both see themselves as leaders. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Market share solution Another form of reaction function; Firm 2 wants to keep a fixed share of k=q2/(q1+q2) in the market. P1=F1(q1,q2) inverse demand for firm 1 Π1=q1F1(q1,q2) – C1(q1) Π1=q1F1(q1,kq1/(1-k)) – C1(q1) dΠ1/dq1=0 q1 , q2 could be found MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Kinked demand curve Conditions ; 1- infrequent price changes 2- firms do not change their price-quantity combinations in response to small shifts of their cost curves. Price decrease will be followed by rivals but price increase would not .Firm would confront with demand curve with different elasticity's . 87 11 26 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Kinked demand curve So marginal revenue curve will be broken. Variation of marginal cost in the broken area of marginal revenue does not change the price. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Kinked demand curve p1 Demand for price increase MC D1 Initial fixed price D Po 85 11 21 Demand for price decrease MR D1 D q1 Q0 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Kinked demand curve An example ; Demand and cost function of the duopolistic model are as follows P1=100 – 2q1 – q2 C1 = 2.5q12 P2=95 – q1 – 3q2 C2=25q2 Currently established price and quantity p1=70 , q1=10 , p2=55 , q2=10 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Kinked demand curve 1- if firm 1 increase his price ,firm 2 would leave his own price unchanged at p2=55. p2=55, (P2=95 – q1 – 3q2) → q2=(40–q1)/3, P1=100 – 2q1 – q2 , p1=(260 - 5q1)/3 So for p1>70 , q1<10 ; p1=(260 - 5q1)/3, MR1=(260-10q1)/3 If q1=10 then MR1=53.33 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition Kinked demand curve imperfect competition 4/26/2017 When P1=100 – 2q1 – q2 , q1=q2 =10 If firm 1 reduce the price , firm 2 will follow in order to maintain his equalshare out of the market , (q1=q2). P1=100 – 3q1 MR1=100 – 6q1 (for P1<70 , q1 >10) In this case when q1=10 , then MR1=40 initial position; p1=70 , MC1 =5q1=50, so; MR1 = 40 < MC1 =50 <MR1 = 53.33. Reduction of marginal cost by more than 10 units or increase in the marginal cost by more Than 3.33 units is needed to change the price . MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition Bilateral monopoly imperfect competition 4/26/2017 Single buyer, single seller It is not possible for the seller to behave as monopolist ,because she can not exploit a buyer’s demand function .The buyer is monopsonist and does not have a demand function and she wants to exploit a point on the seller supply curve. It is not either possible for the buyer to behave as monopsonist , because the buyer can not exploit an input supply function. The seller is a monopolist and does not have a supply function and she wants to exploit a point on the buyer’s demand function. Either one of them should dominate or they may cooperate or market mechanism breaks down. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly 2- Reference solution Market for q2 is the one which will be considered Seller of q2 buys input x, from a competitive market with a price equal to r, for the production of q2 , [q2=h(x) or x=H(q2) ] and sell q2 with a price equal to p2 . Buyer buys q2 with a price equal to p2 and use it as an input to produce q1 and sell q1 in the competitive market with price equal to P1 q1=h(q2) . . MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly A- Monopoly solution Seller of q2 dominate the market and force buyer of q2 to accept whatever price he set. Buyers profit=Πb=p1q1–p2q2 Πb = p1h(q2) - p2q2 dΠb/dq2=p1dh(q2)/dq2 – p2 =0 P2=p1h’(q2)= VMP(q2) MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly The monopolist substitute p2=p1h’(q2) in his profit function to find out how much q2 should he produced: Πs= p1h’(q2) q2 – rx= p1h’(q2)q2–rH(q2) dΠs/dq2 = 0 p1[h’(q2)+h’’(q2)q2] – rH’((q2)=0 p1[h’(q2)+h’’(q2)q2] = rH’((q2) MR(q2)=MC(q2) Point s ; (p2s , q2s), MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MCI Bilateral monopoly p2 p2=rH’(q2) = MC(q2)=s(q2) B P2s S C p2c p1 h’(q2)=VMP(q2)=D(q2) p2b MR(q2) q2 q2b q2s q2c MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly 2-Monopsony solution Buyers dominates the market Sellers profit= Πs =p2q2 – rx = p2q2 – rH(q2) dΠs/dq2=p2 – rH’(q2) = 0 p2 = rH’(q2) price set by buyer=marginal cost of producing q2 Buyer’s profit Πb= p1q1 – p2q2 = = p1h(q2) - rH’(q2)q2 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly dΠb / dq2=p1h’(q2)-r[H’(q2)+H’’(q2)q2]=0 p1h’(q2) = r[H’(q2)+H’’(q2)q2] VMP(q2 in producing q1)=MC of buying q2 for buyer Point B in the figure, q2=q2b, p2=p2b 3 - Seller and buyer are both price taker ( quasi competitive solution ) Supply and demand function are effective ; point c , p2=p2c , q2=q2c P1h’(q2c)=rH’(q2c) VMP(q2 in producing q1)=MC(q2) for seller MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly As a rule ; q2c>q2b , q2c>q2s , but Relation between q2b and q2s is not kwon . It depends to the position (elasticity) of supply and demand curves. In general we expect to have the following results given the same conditions ; P2b<P2c<P2s Πss> Πsc> Πsb seller’ s profit in three cases Πbs< Πbc< Πbb buyer’s profit in three cases MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly 4 - Collusion and bargaining This happens to reach to an agreement on unique price and quantity .This includes two process; 1- determining (q) such that their joint profit is maximized. 2- determining (P) in order to distribute the profit 84 12 2 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly Π=Πb+Πs=[p1h(q2)–p2q2]+[p2q2-rH(q2)] dΠ/dq2=p1h’(q2) – rH’(q2)=0 p1h’(q2)=rH’(q2) (q2=q2c) VMP(q2 in producing q1) = Marginal cost of q2 for seller Quasi-competitive price does not necessarily follow from a collusive solution. The seller wants to put the price as high as possible. Buyer wants to put the price as low as possible. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Bilateral monopoly Different solutions can be found for price (p2); 1- P** <P2<P* Price that force the buyer’s profit to zero = p*= [p1h(q2c)]/q2c Price that force the seller’s profit to zero = p**= [rH(q2c)]/q2c 2- Buyer can do no worse than monopoly situation and seller can do no worse than monopsony solution. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition Bilateral monopoly 4/26/2017 Buyer’s profit in monopoly situation= P1h(q2c) – p2q2c = Πbs P’2=[p1h(q2c) – Πbs] /q2c Seller’s profit in monopsony situation= p2q2c – rH(q2c) = Πsb P’’2=[rH(q2c) + Πsb]/q2c P’’2<P2<P’2 In each case the determination of p2 depends upon the relative power of the bargaining process. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 CAN MONOPOLY BE DEFENDED? Monopoly and Economies of Scale Because monopoly producers are often supplying goods and services on a very large scale they may be better placed to take advantage of economies of scale - leading to a fall in the average total costs of production. These reductions in costs will lead to an increase in monopoly profits but some of the gains in productive efficiency might be passed onto consumers in the form of lower prices. The effect of economies of scale is shown in the diagram. As shown in the following figure economies of scale provide potential gains in economic welfare for both producers and consumers. . 86 11 22 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Monopoly and Innovation (Research and Development) imperfect competition Monopoly and Innovation (Research and Development) 4/26/2017 How are the supernormal profits of monopoly used? Is consumer surplus of equal value to producer surplus? Are large-scale firms required to create a comparative advantage in global markets? Some economists argue that large-scale firms are required to be competitive in international markets. An important issue is what happens to the monopoly profits both in the short run and the long run. Undoubtedly some of the profits will be distributed to shareholders as dividends. This raises questions of equity. Some low income consumers might be exploited by the monopolist because of higher prices. And, some of their purchasing power might be transferred via dividends to shareholders in the higher income brackets - thus making the overall distribution of income more unequal.   However some of the supernormal profits might be used to invest in research and development programs that have the potential to bring dynamic efficiency gains to consumers in the markets. There is a continuing debate about whether competitive or monopolistic markets provide the best environment for high levels of research spending. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

Domestic monopoly but international competition imperfect competition 4/26/2017 Domestic monopoly but international competition A firm may have substantial domestic monopoly power but face intensive competition from overseas producers. This limits their market power and helps keep prices down for consumers. A good example to use here would be the domestic steel industry. Corus produces most of the steel manufactured inside the UK but faces intensive competition from overseas steel producers. MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1

imperfect competition 4/26/2017 Contestable markets! Contestable market theory predicts that monopolists may still be competitive even if they enjoy a dominant position in their market. Their price and output decisions will be affected by the threat of "hit and run entry" from other firms if they allow their costs to rise and inefficiencies to develop.  83 12 4 MICROECONOMICS 1 IMPERFECT COMPETITION MICROECONOMICS 1