Monopoly Quantity & Price Elasticity Welfare. Monopoly Chapter 24

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1 Monopol monopl.gif (GIF Image, 289x289 pixels) Chapter 24

2 Motivating Questions What price and quantit does a monopol choose? What are the welfare effects of monopol? What are the effects of taxes on monopolies? Is monopol ever justified/efficient?

3 What is a monopol? A monopol is a sole supplier of a good. The monopolist s demand curve is the market demand curve. Price maker not a price taker Can set price (quantit is constrained b demand curve relationship) Or: chooses quantit, which determines price

4 What causes monopolies? Legal fiat: US Postal Service Patent: drugs, technolog; intellectual propert Sole ownership of a resource: toll road Cartel: OPEC Large economies of scale: local utilities

5 Government & Monopol Monopol is heavil regulated Antitrust Law: abuse of monopol power is a felon Dept. of Justice (DOJ) has antitrust division Federal Trade Commission (FTC) has regulator oversight But govt. creates monopolies (USPS) and issues patents/coprights that grant monopol power. If if monopol is so bad, wh does the government enable it in some cases?

6 What quantit maximizes profits? Setup the problem: For an firm, profit is given b Π() = R() C(), where R() is revenue and C() is cost. Profit maximization problem: max R() C()

7 Graphical analsis: What quantit maximizes profits? $ R() = p()

8 Graphical analsis: What quantit maximizes profits? $ R() = p() c()

9 Graphical analsis: What quantit maximizes profits? $ R() = p() c() Π()

10 Graphical analsis: What quantit maximizes profits? $ R() = p() c() * Π()

11 Graphical analsis: What quantit maximizes profits? $ R() = p() c() * Π()

12 What quantit maximizes profits? Graphical analsis: $ R() = p() c() * Π() At the profit-maximizing output level, the slopes of the revenue and cost curves are equal:mr( ) = MC( ).

13 What quantit maximizes profits? Algebraic analsis: Optimalit condition: dπ() d = 0 = R () C () = 0 = R () = C () At the profit maximizing quantit, : MR() = MC()

14 What quantit maximizes profits? Algebraic analsis: If the market is competitive, the firm takes p as given/fixed (demand curve is flat) In that case, R() = p, where p is constant, so MR() = p. Profit-maximizing condition: p = MC $ D = MR = p

15 What quantit maximizes profits? Algebraic analsis: Monopol is not a price taker, though Marginal DemandRevenue slopes down curve for a Monopol Recall MR() = P() + P () is below P() price Demand MR

16 What quantit maximizes profits? Algebraic analsis: Choose quantit s.t. MR = MC Set price according to P( ) Example Profit-maximizing on Graphcondition: p = MC Price is marked-up over marginal cost p > MC price MC p m = 8 MC = MR m =2 MR Demand

17 Monopol: Example Inverse Demand: P() = 10, so marginal revenue is MR() = Cost function: C() = 2 + 2, so MC() = Optimalit condition: So m = 8 4 = 2 MR = MC = 10 2 = and p m = P( m ) = 10 2 = 8

18 Example on Graph Monopol: Example price MC p m = 8 MC = MR m =2 MR Demand

19 Monopol Price and Elasticit of Demand How does the monopol price relate to the elasticit of demand? MR = p() + dp() d = p()[1 + dp() p() d ] Recall that So ɛ = p() d dp(). MR = p()[1 + 1 ɛ ].

20 Monopol Price and Elasticit of Demand How does the monopol price relate to the elasticit of demand? MR = p()[1 + 1 ɛ ] and MR = MC, so MC = p()[1 + 1 ɛ ]. Rewrite as p() = MC ɛ Note that MR, p > 0 implies ɛ < 1 This means that a monopolist chooses an output level at which demand is elastic. Intuition: if on inelastic part, cutting output (raising price) increases revenue (and mabe lowers costs)

21 Monopol Price and Elasticit of Demand How does the monopol price relate to the elasticit of demand? p() = MC ɛ Because elasticit is negative (demand slopes down), price is alwas above MC Markup pricing: price is marginal cost plus a markup. What happens to the markup as demand becomes less elastic? Monopolist increases price Example: if ɛ = 3, p() = 3MC 2 ; if ɛ = 2, p() = 2MC

22 Perfect Competition vs. Monopol Perfect Competition versus Monopol Price and Quantit: given a cost function, how does the behavior of a monopolist compare to that of a competitive firm? price MC p m p c MR Demand m c p m > p c and m < c

23 Inefficienc of Monopol What are the welfare effects of monopol? Who gains and who loses? Since p m > p c, seller gains, consumers lose But since m < c, we know that there are unrealized gains from trade. So the losses outweigh the gains: there is some welfare loss. The deadweight loss (DWL) is the societal loss in welfare. It measure the inefficienc of monopol relative to the competitive outcome.

24 Calculating Calculating Deadweightthe Loss DWL of Monopol of Monopol price In competitive equilibrium Consumer surplus = A + B+ C p m p c A B C MC Demand m c MR

25 Calculating Calculating Deadweightthe Loss DWL of Monopol of Monopol price In competitive equilibrium Producer surplus = D + E p m p c A D B C E MC MR Demand m c

26 Calculating Calculating Deadweightthe Loss DWL of Monopol of Monopol price In competitive equilibrium Total surplus = A + B + C + D + E p m p c B D A C E MC MR Demand m c

27 Calculating Calculating Deadweightthe Loss DWL of Monopol of Monopol price In Monopol case Producer surplus = B + D p m p c A BB D C E MC MR Demand m c

28 Calculating Calculating Deadweightthe Loss DWL of Monopol of Monopol price In Monopol case Consumer surplus = A p m p c A B C MC Demand m c MR

29 Calculating Calculating Deadweightthe Loss DWL of Monopol of Monopol price In Monopol case Total surplus = A + B + D DWL = (A + B + C + D + E) (A + B + D) = C + E p m p c MC( m ) A BB D C E MR MC Demand m c

30 Inefficienc of Monopol The need for regulation Competitive market provides greater surplus than monopol Can changing from a monopolistic market to a competitive one make everone (consumers and monopolist) better off (Pareto improving)? In other words, is there room for a Pareto improving deal in which a monopolist agrees to act like a competitive firm? No, because this will make the firm worse off Thus, the DWL of monopol rationalizes antitrust laws

31 Example (continued) Inverse demand: P() = 10 Marginal cost: MC() = Recall: p m = 8 and m = 2 What is the competitive equilibrium? Use p = MC P( c ) = 10 c = = MC( c ) So c = 8 3 and pc = 22 3

32 Example (continued) So what is the DWL of monopol? We can calculate DWL using DWL = 1 2 [P( m ) MC( m )][ c m ] Aside: in general, this is an approximation. Because of linear demand, MC, here it is exact. So DWL is DWL = 1 2 [8 6][8 3 2] = 2 3

Chapter 15: Monopoly WHY MONOPOLIES ARISE HOW MONOPOLIES MAKE PRODUCTION AND PRICING DECISIONS

Chapter 15: Monopoly WHY MONOPOLIES ARISE HOW MONOPOLIES MAKE PRODUCTION AND PRICING DECISIONS Chapter 15: While a competitive firm is a taker, a monopoly firm is a maker. A firm is considered a monopoly if... it is the sole seller of its product. its product does not have close substitutes. The