ECON191 (Spring 2011) 27 & 29.4.2011 (Tutorial 9) Chapter 10 Market Power: Monopoly an Monosony Monopoly: market with only one seller a Deman function, TR, AR, an P p=a bq ( q) AR( q) for all q except q = 0. In orer to sell 1 extra unit, the monopoly must lower the price for that extra unit as well as for the previous units. There is an exact relationship between an AR. Slope of is twice as steep as the slope of DD (AR). =a 2bq AR=DD Q Suppose we have a linear inverse DD function: p a bq TR( q) ( q) q 2 TR( q) p( q) q aq bq a 2bq Slope of is 2b while slope of DD is b. Profit Maximization of a monopoly P MC The monopolist is facing a maximizing problem. Given: Deman function: P(Q) Total cost function: C(Q) P* DD A monopolist s objective is to maximize profit. Q* A monopoly will never price a commoity on the inelastic portion of the eman curve The more inelastic the eman, the larger the ivergence between MC an P. (The higher the ability the monopolist to charge a price above MC) The steeper the eman curve, the higher the monopoly power 1
Example: (P.347) Suppose the cost of prouction is C(Q) = 50 + Q 2 an the eman is given by P(Q) = 40 Q. Fin the monopoly price, quantity an the level of profit. The monopolist s profit is maximize when = MC Deman curve is given by P(Q) = 40 Q, thus = 40 2Q 2 C( Q) Total cost isc( Q) 50 Q,thus MC = 2Q Q Equating an MC, 40 2Q = 2Q Q* = 10, P* = 30 Profit = 300 150 = 150 Monopoly power an the price elasticity of eman Price elasticity of eman (facing the firm): (What is the interpretation?) A monopoly s profit is maximize when = MC, when P( Q) MC( Q) E The price charge by the monopolist inversely relate to E. The above expression shows that when E, = P. That means the more inelastic the eman (the smaller the absolute value of E ), the larger the ivergence between MC an P. (The higher the ability the monopolist to charge a price above MC) The steeper the eman curve, the higher the monopoly power A firm s market power epens on the elasticity of market eman, the level of competition, number of firms in the market, etc. Elasticity of market eman positively affects the elasticity of eman facing the firm The more competitive the market is, the larger the absolute value of E 2
Measuring monopoly power: Lerner s inex Measure of monopoly power calculate as excess of price over MC (0 < L < 1) High monopoly power oes not necessarily imply high profit, it epens on AC relative to price Example: Supermarkets an convenience stores (P.358) Supermarkets: several firms selling similar proucts No single supermarket can raise its price very much without losing customers to other stores The elasticity of eman for iniviual supermarket: 10 P = MC/(1 0.1) = 1.11MC Lerner inex: (P MC)/P = 1/E = 0.1 Convenience stores: charge a higher price than supermarkets (less elastic eman) The elasticity of eman for iniviual supermarket: 5 P = MC/(1 0.2) = 1.25MC Learner inex: (P MC)/P = 1/E = 0.2 Convenience stores have more monopoly power. Convenience stores o not have higher profits than supermarkets however, as volume is far smaller an average fixe costs are larger Welfare implications an socially optimal price an quantity P CS MC We measure the welfare of the society by consumer surplus an proucer surplus. PS p* DWL Consumer surplus: total willingness to pay actual payment Prouce surplus: total revenue total variable cost Total surplus: (CS + PS) q* DD Following the profit maximizing rules: monopolist s profit is maximize, however it is not socially optimal. (Since at q *, p>mc). A kin of ea weight loss is generate. From the society point of view, the price is too high an the quantity is too little. Other issues: rent seeking, price regulation 3
The multi-plant firm For some firms, prouction takes place in more than one plant each with ifferent costs. Firm must etermine how to istribute prouction between both plants Prouction shoul be split so that the MC in the plants is the same. Output is chosen where = MC. Profits is maximize when = MC at each plant Total output: Total profit: Firm shoul increase output from each plant until the aitional profit from last unit prouce at Plant 1an Plant 2 equals 0 Similarly, for Plant 2, The firm shoul prouce so that Example: Chapter 10 Problem 9 A rug company has a monopoly on a new patente meicine. The prouct can be mae in either of two plants. The costs of prouction for the two plants are MC 1 = 20 + 2Q 1, an MC 2 = 10 + 5Q 2. The firm s estimate of the eman for the prouct is P = 20-3(Q 1 + Q 2 ). How much shoul the firm plan to prouce in each plant? At what price shoul it plan to sell the prouct? From the iagram, we see that only MC 2 is relevant because MC 1 lies above the eman curve. Price 30 20 17.3 10 MC 2 = 10 + 5Q 2 MC 1 = 20 +2Q 1 DD: P = 20 3Q 2. = 20 6Q 2. To etermine the profit-maximizing level of output, equate an MC 2 : 20 6Q 2 = 10 + 5Q 2, or Q = Q 2 = 0.91 P = 20 3(0.91) = 17.3 0.91 D 3.3 6.7 Q 4
Natural monopoly an regulation Natural monopoly: A firm that can prouce the entire output of an inustry at a cost lower than what it woul be if there were several firms. It usually arises when there are large economies of scale Splitting the market into two firms results in higher AC for each firm than when only one firm was proucing Unregulate, the monopolist woul prouce Q m an charge P m. If the price were regulate to be P c, the firm woul lose money an go out of business. Setting the price at P r giving profits as large as possible without going out of business It is very ifficult to estimate the firm's cost an eman functions because they change with evolving market conitions. (Alternatives?) Rate of return regulation: the firms to set a maximum price base on the expecte rate or return that the firm will earn. Regulatory agencies often use to etermine price Problems: (1) Firm s capital stock is ifficult to value, (2) Fair rate of return base on actual cost of capital, that cost is base on regulatory behavior an investor s perception of allowe rates in the future (3) Time lags in regulatory response to changes in cost an other market conitions Price Cap set base on firms variable costs, past prices, an possibly inflation an prouctivity growth A firm is typically allowe to raise its price each year without approval from regulatory agency by amount equal to inflation minus expecte prouctivity growth 5
Monopsony Monopsony: a market in which there is a single buyer. Monopsony power is the ability of the buyer to affect the price of the goo an pay less than the price that woul exist in a competitive market. Marginal value: the aitional benefit erive from purchasing one more unit of a goo Deman curve is the MV curve Average expeniture: the aitional cost of buying one more unit of a goo Supply curve is the AE curve as it shows how much must be pai per unit Marginal expeniture: the aitional cost of buying one more unit of a goo Upwar sloping supply implies the ME curve must lie above AE If a buyer wants to buy one more unit, he has to pay a higher price for that unit as well as for the previous units. Total expeniture = Marginal expeniture = (What is the interpretation?) Typically a monopsony chooses to buy until the benefit from last unit equals that unit s cost Marginal value = Marginal expeniture (MV = ME) Monopsony power Price elasticity of supply (facing the firm): A monopsony s benefit is maximize when MV = ME 6
Measure of monopsony power calculate as excess of MV over price (0 < L < 1) The smaller the elasticity of supply facing the buyer, the higher the monopsony power to mark own the price (pay a price lower than MV) The egree of monopsony power epens on the elasticity of market supply, number of buyers, interaction among buyers, etc Example: Chapter 10, Problem 14 The employment of teaching assistants (TAs) by major universities can be characterize as a monopsony. Suppose the eman for TAs is W = 30,000-125n, where W is the wage (as an annual salary), an n is the number of TAs hire. The supply of TAs is given by W = 1000 + 75n. (a) If the university takes avantage of its monopsonist position, how many TAs will it hire? What wage will it pay? Supply curve = Average expeniture curve: W = 1000 + 75n Total Expeniture = AE(n)75n 2 = 1000n + 75n 2 Marginal Expeniture = TE/n = 1000 + 150n A monopsonist, the university woul equate marginal value (eman) with marginal expeniture to etermine the number of TAs to hire: 30000 125n = 1000 + 150n n = 105.5 Substituting n = 105.5 into the supply curve to etermine the wage: 1000 + (75)(105.5) = $8909 annually (b) If, instea, the university face an infinite supply of TAs at the annual wage level of $10,000, how many TAs woul it hire? With an infinite number of TAs at $10000, the supply curve is horizontal at $10000. Total expeniture is 10000n, an marginal expeniture is 10000. Equating marginal value an marginal expeniture: 30000 125n = 10,000 n = 160 Comparing Monopoly an Monopsony Monopoly < P ( below the eman, AR) P > MC Q M < Q C (competitive quantity) P M > P C (competitive price) Monopsony ME > P ( ME above the supply, AE) P < MV Q M < Q C (competitive quantity) P M < P C (competitive price) 7