ECON 330 Lecture 8 Thursday, October 11

HWKs HWK #2 is due next Tuesday in class. Working in groups is fine but please write your own answers. NO direct COPYING from friends.

MONOPOLY Equlibrium. Inefficiency of market power The dominant firm model Estimating the inefficieny of market power

A monopoly faces a downward sloping demand curve. A firm is a monopoly if it is the only supplier of a product for which there is no close substitute. A monopoly faces a downward sloping demand curve. This means that to sell a larger quantity the monopoly must lower the price. contrast this with the competitive firm which can sell any quantity at the given market price.

A little bit of mathematics: Solving the monopoly model Let Q(P) be the (market) demand curve for the monopoly firm’s product. We can define the inverse demand as P(Q). Example: Demand Q(P) = 10 – 2P Inverse demand P(Q) = 5 – 0.5Q

The demand, an example from last lecture Q P 2,70 7,00 2,85 6,75 3,02 6,50 3,20 6,25 3,40 6,00 3,63 5,75 3,88 5,50 4,16 5,25 4,47 5,00

Profit maximization Profit = revenue – cost = P(Q)·Q – C(Q) Choose Q to maximize profits or Profit = P·Q(P) – C(Q(P)) Choose P to maximize profits

Differentiate, set equal to 0! Profit = P(Q)∙Q – C(Q) The derivative of the total revenue P(Q)∙Q with respect to Q is d[P(Q)∙Q]/dQ = [dP/dQ]∙Q + P This is the product rule of differentiation: The derivative of two functions f(x) ∙ g(x) with respect to x is f’ ∙ g + f ∙ g’

Profit = P(Q)∙Q – C(Q) The derivative of the cost function C(Q) with respect to Q is MC(Q) (marginal cost)

Profit = P(Q)∙Q – C(Q) So when we take the derivative of profits with respect to Q and set equal to 0 we have [dP/dQ]∙Q + P – MC = 0

But what is this condition But what is this condition? [dP/dQ]∙Q + P – MC = 0 The first two terms together are the MARGINAL Revenue. The last term is the Marginal Cost. The condition says: to max profits choose Q such that MR equals MC.

MR defined as ΔTR/ΔQ AC = MC = 2. Example continued MR defined as ΔTR/ΔQ AC = MC = 2.

A few words on MR MR ≡ P + Q(dP/dQ) dP/dQ < 0, so MR < P (always). dP/dQ < 0 means that to sell a larger quantity the monopoly must lower its price. contrast with the competitive firm which can sell any quantity at the given market price

Some algebra to rearrange the condition [dP/dQ]∙Q + P – MC = 0 into (P – MC)/P = –1/EP

[dP/dQ]∙Q + P – MC = 0 P – MC = –[dP/dQ]∙Q (P – MC)/P = –[dP/dQ]∙Q/P Recall The Price elasticity (of demand) formula EP = [ΔQ/Q]/[ΔP/P] = [ΔQ/ΔP]/[P/Q] So [dP/dQ]∙Q/P ≡ 1/EP The profit maximization condition for monopolist says MR = MC, or (P – MC)/P = –1/EP

Interpreting (P – MC)/P = –1/EP The degree of monopoly power depends on the demand elasticity. A Monopoly Firm that faces highly elastic demand (say, EP = -5) cannot raise price much above MC. A Monopoly Firm that face less elastic demand (say, EP = -2) can raise price above MC.

More mathematics: An example with linear demand The inverse demand is p(Q) = a – bQ The total revenue is TR(Q) = p(Q)Q = aQ – bQ2 MR is the derivative of TR with respect to Q So MR(Q) = a – 2bQ Note MR(Q) < p(Q) = a – bQ for Q > 0.

Marginal revenue curve with linear demand p(Q) = a – bQ Q a/2b a/b MR(Q) = a – 2bQ

Cost functions The total cost function be TC(Q) = F + αQ + βQ2 The marginal cost MC is the derivative of TC with respect to Q So MC(Q) = α + 2βQ

Marginal Cost $ TC(Q) = F + αQ + β Q2 F Q $/output unit MC(Q) = α + 2βQ α Q

MR(Q*) = MC(Q*). Finding the Q* At the profit-maximizing output level Q*, MR(Q*) = MC(Q*). So if p(Q) = a – bQ and TR(Q) = aQ – bQ2, and TC(Q) = F + αQ + βQ2 then MR = a – 2bQ MC = α + 2βQ The profit maximizing output level is defined by a – 2bQ = α + 2βQ and is Q* = (a–α)/2(b+β)

The monopoly equilibrium on the graph $/output unit p(Q) = a - bQ MC(Q) = α + 2βQ y MR(Q) = a - 2bQ

The Inefficiency of Monopoly Now… The Inefficiency of Monopoly

A few definitions Social welfare is measured by the sum of Consumer Surplus and Producer Surplus.

Efficiency defined A market outcome is efficient if the sum of consumer surplus (CS) and producer surplus (PS) is at a maximum. CS+PS is also known as Social Welfare. In that sense the equilibrium of the competitive market is efficient. In that sense the equilibrium of the monopoly market is not efficient.

On a demand and supply graph the CS is shown as the are under the demand curve above the price line for quantity levels from 0 to the equilibrium quantity. The PS is shown as the are above the supply (or the marginal cost) curve under the price line for quantity levels from 0 to the equilibrium quantity.

The efficiency of the competitive equilibrium $/output unit The efficient output level Qe satisfies p(Q) = MC(Q). Total gains-to-trade is maximized. p(Q) CS MC(Q) p(Qe) PS Qe Q

The Inefficiency of Monopoly $/output unit p(Q) CS p(Q*) MC(Q) PS Q* Q MR(Q)

The Inefficiency of Monopoly $/output unit The monopoly produces less than the efficient quantity, the monopoly rice exceeds the efficient (competitive) price. p(Q) p(Q*) MC(Q) DWL p(Qe) Q* Qe Q MR(Q)

The in-class exercise The Dead Weight Loss of Monopoly

In class exercise A well known book publishing company has the rights to the latest Orhan Pamuk novel. There are three different groups of potential buyers out there. A group of 10,000 Pamuk-crazy readers will pay up to 20 liras for the book. Another group of 30,000 people will buy the book if it costs not more than 15 liras. The third group of 50,000 readers will pay only up to 9 liras. a. What price will maximize profits, if it costs 5 liras to print and distribute one book? b. Compute the deadweight loss when profits are maximized. If you have time think about the following What price will maximize the number of books sold while at the same time giving the company a 5% profit on total cost, which includes the 150,000 liras payment to Mr. Pamuk?

DWL

The profit maximizing price is 15, the first two groups will buy, the third group will not. CS = 10,000x(20 – 15) + 30,000x(15 – 15) = 50,000 PS = (15 – 5)x40,000 = 400,000 Social welfare = 450,000

DWL = 50,000x(9 – 5) = 200,000 This is the surplus that could be realized by selling the book to the third group at any price between 5 and 9.

Sell 90,000 books. Cost = 90,000x5+150,000 = 600,000. With 5% profit this means you need 630,000 in revenues, which means that you should sell the book for 7.