a dominant firm with a competitive fringe(2 Let the supply function of the competitive fringe be given by Q =Q (p), where p is the price charged by the dominant firm Suppose that the market demand function is Qm=Qm(p). Then the residual demand of the dominant supplier is the difference between market demand and the supply of the fringe QD(p)=om(p)-Qt(p). the residual demand for the dominant firm shows its sales for any price it charges. It is an example of a firms demand function the difference between market demand and the dominant firms demand is the supply response of the competitive fringe The profits of the dominant firm are TTD=pQ (p)-C(Q(p)) dirD/dp=QD+pdQD/dp-dcldQd)(dQ/dp A profit-maximizing firm would set its price such that the rate of change of its profits with respect to its price equals zero, or: QD+[p-dcldQd)I(dQd/)=0 Increase in its price leads to a reduction in demand for 2 reasons 1. Increasing the price makes it profitable for the price-taking fringe to expand their output, reducing the residual demand of the dominant firm 2. The quantity demanded in the market decreases as the price increases dQD/dp=dQm(p)/dp-dQt(p)/dp QD+[p-dc/dQD)I[dQm(p)/dp-dQt(p)/dp]=o, where dQm(p)/dp is the reduction in market demand from a price increase and dQ (p)/dp is the increase in fringe supply
A dominant firm with a competitive fringe (2) • Let the supply function of the competitive fringe be given by Qf=Qf (p), where p is the price charged by the dominant firm. Suppose that the market demand function is Qm=Qm(p). Then the residual demand of the dominant supplier is the difference between market demand and the supply of the fringe: QD(p)=Qm(p)-Qf (p). The residual demand for the dominant firm shows its sales for any price it charges. It is an example of a firm’s demand function: the difference between market demand and the dominant firm’s demand is the supply response of the competitive fringe. • The profits of the dominant firm are: • πD=pQD(p)-C(QD(p)). • dπD/dp=QD+pdQD/dp-(dC/dQD)(dQD/dp). • A profit-maximizing firm would set its price such that the rate of change of its profits with respect to its price equals zero, or: QD+[p-(dC/dQD)] (dQD/dp)=0. • Increase in its price leads to a reduction in demand for 2 reasons: • 1. Increasing the price makes it profitable for the price-taking fringe to expand their output, reducing the residual demand of the dominant firm. • 2. The quantity demanded in the market decreases as the price increases. • dQD/dp=dQm(p)/dp-dQf (p)/dp • QD+[p-(dC/dQD)] [dQm(p)/dp-dQf (p)/dp]=0, where dQm(p)/dp is the reduction in market demand from a price increase and dQf (p)/dp is the increase in fringe supply
a dominant firm with a competitive fringe( 3) LD=*MC(QVp*=s/(Ess+E), where L is the Lerner index for the dominant firm, MC(Q*)its marginal cost at the profit-maximizing price * and quantity Q* s its market share s the market share of the fringe, es the elasticity of supply of fringe and ethe elasticity of market demand The market power of the dominant firm is determined by 3 factors 1. The elasticity of market demand. The greater the elasticity of demand the less market power the dominant firm can exercise since consumers'willingness to substitute to other products is greater 2. The elasticity of supply of the fringe. The greater the supply response of the competitive fringe the lower the market power of the dominant firm. Attempts by the dominant firm to raise price are less profitable the greater the ability of the fringe to provide consumers with opportunities for supply substitution. The elasticity of fringe supply depends on the behavior of marginal cost: the more it is inelastic with respect to output-the less it increases as output increases-the larger the fringe elasticity of supply 3. The more efficient the dominant firm vis-a-vis the fringe- the lower its marginal costs-the greater its market power
A dominant firm with a competitive fringe (3) • L D=[p*-MC(Q*)]/p*=sD/(εs fs f+ε), where L D is the Lerner index for the dominant firm, MC(Q*) its marginal cost at the profit-maximizing price p* and quantity Q*, sD its market share, s f the market share of the fringe, εs f the elasticity of supply of fringe, and εthe elasticity of market demand. • The market power of the dominant firm is determined by 3 factors: • 1. The elasticity of market demand. The greater the elasticity of demand, the less market power the dominant firm can exercise since consumers’ willingness to substitute to other products is greater. • 2. The elasticity of supply of the fringe. The greater the supply response of the competitive fringe, the lower the market power of the dominant firm. Attempts by the dominant firm to raise price are less profitable the greater the ability of the fringe to provide consumers with opportunities for supply substitution. The elasticity of fringe supply depends on the behavior of marginal cost: the more it is inelastic with respect to output-the less it increases as output increases-the larger the fringe elasticity of supply. • 3. The more efficient the dominant firm vis-à-vis the fringe-the lower its marginal costs-the greater its market power
a dominant firm with a competitive fringe(4) There is also an endogenous relationship between market power and market share. the larger the dominant firms market share the greater its market power, holding everything else constant. This model provides some support for the proposition that larger market shares suggests market power, provided it is understood that such a comparison involves holding constant the elasticity of demand and the fringe's elasticity of supply If there is no fringe, then s=0, s=1, and Es=0 and we get the usual condition for profit maximization by a monopolist the lerner index equals the inverse of the market elasticity of demand L=1/E
A dominant firm with a competitive fringe (4) • There is also an endogenous relationship between market power and market share. The larger the dominant firm’s market share the greater its market power, holding everything else constant. This model provides some support for the proposition that larger market shares suggests market power, provided it is understood that such a comparison involves holding constant the elasticity of demand and the fringe’s elasticity of supply. • If there is no fringe, then s f=0, s D=1, and εs f=0 and we get the usual condition for profit maximization by a monopolist: the Lerner index equals the inverse of the market elasticity of demand L=1/ε
Qt(p) QD(p=Qm(p)-Q(p) MCD MRD Qm(p) MRD MCD1 Qf QD=Q*Qm QD(p) Dominant firm with competitive fringe
Qm(p) MRD MCD 1 Qf (p) MCD MRD QD(p)=Qm(p)-Qf (p) p max p* p 0 Qf QD=Q*Qm QD(p0 ) Dominant firm with competitive fringe
a dominant firm with a competitive fringe(5) In figure, the residual demand QD remaining for the dominant firm at any price p is the difference between market demand Qm and the fringe supply The dominant firm's demand curve is found by shifting the market demand curve to the left by the amount of the fringes supply If the dominant firm sets a price equal to or greater than pmax, its residual demand will be zero. At pmax and above prices are sufficiently high that the fringe finds it profit maximizing to at least produce enough to meet demand For prices below po, the fringe finds it profit maximizing to shut down at price po the fringe firms are indifferent between not producing any output and producing at the minimum of their average avoidable cost curves For prices less than po residual demand is the same as market demand. at prices below pu, the dominant firm can safely ignore the fringe in making price decision The dominant firms marginal revenue curve, MR, is marginal to the residual demand not market demand- unless price is less than po, in which case market demand and residual demand are the same this means that the marginal revenue curve will jump down when the dominant firm considers increasing its output above QD(po) The profit-maximizing quantity Q* satisfies MRD(Q*)=MCD(Q*)
A dominant firm with a competitive fringe (5) • In figure, the residual demand QD remaining for the dominant firm at any price p is the difference between market demand Qm and the fringe supply Qf . • The dominant firm’s demand curve is found by shifting the market demand curve to the left by the amount of the fringe’s supply. • If the dominant firm sets a price equal to or greater than pmax, its residual demand will be zero. At pmax and above, prices are sufficiently high that the fringe finds it profit maximizing to at least produce enough to meet demand. • For prices below p0 , the fringe finds it profit maximizing to shut down. At price p0 the fringe firms are indifferent between not producing any output and producing at the minimum of their average avoidable cost curves. For prices less than p0 residual demand is the same as market demand. At prices below p0 , the dominant firm can safely ignore the fringe in making price decision. • The dominant firm’s marginal revenue curve, MRD, is marginal to the residual demand, not market demand-unless price is less than p0 , in which case market demand and residual demand are the same. This means that the marginal revenue curve will jump down when the dominant firm considers increasing its output above QD(p0 ). • The profit-maximizing quantity Q* satisfies MRD(Q*)=MCD(Q*)