EconS Monopoly - Part 2

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1 EconS Monopoly - Part 2 Eric Dunaway Washington State University eric.dunaway@wsu.edu October 26, 2015 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

2 Introduction Last time, we covered monopoly equilibrium behavior and saw how prices and quantities compare to their perfectly competitive counterparts. The monopolist produces less quantity at a higher price and earns positive economic pro ts. Today, we will analyze welfare e ects of monopoly, and how monopolists mark up their prices. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

3 Welfare Today should feel a bit like a review of welfare as we apply it to the monopoly market. We ll be looking at our triangle and trapezoid formulas again. Monopoly is a signi cant source of dead weight loss on a market. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

4 Welfare p D S 0 Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

5 Welfare p D S p C 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

6 Welfare p D S p C Consumer Surplus Producer Surplus 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

7 Welfare Recall that the triangle underneath the demand curve, but above the equilibrium price is our consumer surplus, which measures the welfare level of the buyers, and the triangle above the supply curve, but below the equilibrium price is our producer surplus, which measures the welfare level of the sellers. Let s see how these change under monopoly. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

8 Welfare p D S p C 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

9 Welfare p D S p C MR 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

10 Welfare p D S p M p C MR Q M 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

11 Welfare p D S p M CS DWL p C Producer Surplus MR Q M 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

12 Welfare Clearly, the consumer surplus falls and the producer surplus rises. When the monopolist charges a price higher than marginal cost, it "steals" surplus from the consumers, while at the same time causing a dead weight loss. The dead weight loss exists because price is higher than marginal cost. There are consumers who would gladly pay a price higher than the cost to produce the next unit, but not the monopolist s price. The monopolist can t sell to them unless he lowered the price for everyone, which he won t. If only he could price discriminate (Friday!). Let s look at the changes graphically. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

13 Welfare p D S p C Consumer Surplus Producer Surplus 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

14 Welfare p D S p M CS DWL p C Producer Surplus MR Q M 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

15 Welfare p p M p C D CS Stolen Surplus Producer Surplus Surplus lost by the Consumer MR Surplus lost by the Producer S Q M Q C 0 Q C Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

16 Welfare In this scenario, as opposed to when we rst studied welfare, the monopolist always gains producer surplus. Recall that it was possible that the rm could lose surplus if the producer s share of dead weight loss was grater than the "stolen" surplus. A monopolist will keep this from happening. Let s look at a numerical example. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

17 Example Consider a monopolist who faces a linear inverse demand curve p = 24 q and a total cost curve of TC = 12 + q 2 First, let s look at the monopolist s quantity, price and pro t level if he behaved as if he were in a perfectly competitive market. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

18 Example p = 24 q TC = 12 + q 2 Remember that in perfect competition, p = MC. Our marginal cost is MC = 2q and since our price comes from our inverse demand curve, we just set them equal to one another p = MC 24 q = 2q 3q = 24 q C = 8 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

19 Example p = 24 q TC = 12 + q 2 q C = 8 Plugging this back in to the inverse demand function gives a price of p C = 24 q C = 16 Putting them together, our total revenue is as opposed to a total cost of which yields equilibrium pro ts of TR C = p C q C = 16(8) = 128 TC C = 12 + (q C ) 2 = = 76 π C = TR C TC C = = 52 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

20 Example Why are there pro ts in equilibrium? This is just a consequence of the single rm. With no other rms, the monopolist produces the whole market output, getting some nice economic pro ts. If this were an actual competitive market, more rms would enter, causing the rms demand curve to be at and the pro ts will disappear. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

21 Example p 24 D S Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

22 Example Let s calculate the welfare levels. Using our triangle rules, CS C = 1 2 (pmax p C )q C = 1 (24 16)8 = 32 2 PS C = 1 2 (pc p MIN )q C = 1 (16 0)8 = 64 2 W C = CS C + PS C = = 96 These numbers should make sense. Since the supply curve is steeper than the demand curve, the producer surplus should be greater than the consumer surplus. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

23 Example p 24 D S 16 CS PS Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

24 Example Now, let s see what the monopolist will do if he were acting as a monopolist. First, we need his marginal revenue, TR = pq = (24 q)q = 24q q 2 MR = 24 2q Then, we set MR = MC to nd our equilibrium quantity, MR = MC 24 2q = 2q 4q = 24 q M = 6 and our monopoly quantity is less than our perfectly competitive quantity, which we should expect. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

25 Example Plugging our equilibrium quantity back into the inverse demand function gives our equilibrium price, p M = 24 q M = 24 6 = 18 which is higher than our perfectly competitive price, as expected. With these two values we can calculate our total revenue and total cost TR M = p M q M = 18(6) = 108 TC M = 10 + (q M ) 2 = = 46 which leads to the equilibrium pro ts of π M = TR M TC M = = 62 This pro t level is also higher than the perfectly competitive counterpart. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

26 Example p 24 D S Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

27 Example Lastly, we need to calculate our welfare values. Let s look at it graphically rst. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

28 Example p D CS S PS DWL Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

29 Example We can use the triangle formula to calculate our consumer surplus, CS M = 1 2 (pmax p M )q M = 1 (24 18)6 = 18 2 To get the producer surplus, we need to use a trapezoid formula, PS M = 1 2 (pm p MIN + b 2 )q M where b 2 is the vertical distance between the demand and supply curves when we plug the equilibrium quantity in. p D = 24 q M = 24 6 = 18 p S = 2q M = 2(6) = 12 b 2 = p D p S = 6 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

30 Example Plugging the numbers in, PS M = 1 2 (pm p MIN + b 2 )q M = 1 ( )6 = 72 2 which gives total welfare of W M = CS M + PS M = = 90 To get the dead weight loss, we just take the di erence between the welfare from perfect competition and the welfare from monopoly, DWL = W C W M = = 6 and thus 6 dollars of surplus is lost from this market due to the monopolist. Let s see an alternative way. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

31 Example Suppose we didn t know the perfectly competitive welfare level. We could get the dead weight loss with another triangle formula. The base would be equal to the same base as in our producer surplus trapezoid, b 2. The height would be the di erence between the competitive quantity and the monopoly quantity. In other words, DWL = 1 2 b 2(q C q M ) = 1 (6)(8 6) = 6 2 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

32 Example Thus, as we can see, the producer surplus increases under monopoly, the consumer surplus decreases under monopoly, and we get dead weight loss. Since there exists dead weight loss, we would consider this a market failure. All this means is that there is something ine cient going on in the market, and if some outside force (like the government) could step in and correct it, welfare would improve. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

33 Market Power Another thing that economists (regulators) are interested in when looking at monopoly pricing is how much market power a rm has. By market power, I mean how much the rm can charge above the perfectly competitive price, marginal cost. The atter the demand curve, the less market power a monopolist has. With more market power, the monopolist creates more dead weight loss by increasing its price. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

34 Market Power p MC (S ) p M p C MR Q M Q C D Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

35 Market Power p MC (S ) p M p C MR Q M Q C D Q Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

36 Market Power Where does market power come from? It depends on how vital the monopolist s product is to the market. If there are close substitutes, people could pick other products (Monopolistic Competition). If more rms are able to enter into the market, the monopolist would lose power (Oligopoly). Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

37 Market Power Also, we could have a situation where we have a local monopoly. This would be where the rm is a monopoly just in their limited area. Walmart, gas station in a small town, etc. If competitors relocated closer to the monopolist, their market power would be reduced. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

38 Market Power Recall that the steepness of the demand curve is related to its elasticity. A more elastic (ε < 1) demand curve is atter, while a less elastic ( 1 < ε 0) is steeper. If we could gure out a way to express marginal revenue in terms of elasticity, this would make for a great analysis. Of course we can. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

39 Market Power There is an alternative way to express the marginal revenue curve MR = p + p q q This comes from graphically looking at the change in revenue that a monopolist observes when it lowers its price. It comes from a calculus de nition. Figure 11.1 in Perlo s Book has the graphical derivation. We can manipulate this function mathematically to put it in terms of the elasticity. Note: This derivation is just for completeness. I would never ask you to derive this on an exam. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

40 Market Power MR = p + p q q I am going to multiply the second term by p p. I can do this since it is equal to 1 and I haven t changed its value MR = p + p p p q q = p + p p q q p Remember the de nition of price elasticity of demand ε = q p p q thus, if I take the reciprocal of both sides, 1 ε = p q q p which is that last term in our marginal revenue equation Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

41 Market Power MR = p + p p q q p Substituting in our elasticity expression, MR = p + p ε and factoring out the p, MR = p ε This puts the marginal revenue in terms of price and the price elasticity of demand, which is really useful to tell us about market power. Let s look at the equilibrium. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

42 Market Power In equilibrium, marginal revenue equals marginal cost, MR = p = MC ε p If we solve for MC, this term is known as markup rule, which tells us the ratio above marginal cost that the monopolist charges. p MC = ε = ε ε + 1 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

43 Market Power Under perfect competition, marginal cost. p MC = 1, and there is no markup over This is because under perfect competition, the demand function is perfectly elasting (ε = ) and 1 = 0. As the demand becomes less elastic, the markup increases, indicating an increase in market power. For example, when ε = 2 (fairly elastic) p MC = = 2 and the monopolist will charge double the marginal cost for his price. Note: The monopolist will never produce where the demand curve is inelastic. In this case, he could increase his pro ts by reducing his price (and he would). Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

44 Market Power We can rearrange the terms again to get the following relationship p MC p = 1 ε This is known as the Lerner Index, and is a common measurement of market power used in policy making. Again, under perfect competition, the Lerner index is equal to 0, since = 0 and intuitively if p = MC, then p MC = 0. 1 Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

45 Summary Monopoly causes market failure. The more market power that a monopolist has, the more distortion it causes to the markets. This leads to a higher markup price. We can gure out how much market power a monopolist has based on the price elasticity of demand. Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

46 Preview for Wednesday Monopoly regulation. How do governments intervene in monopoly markets to restore e ciency? Applications of monopoly. When would monopolists want to produce more than the standard monopoly output? Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47

47 Assignment 5-4 (1 of 1) 1. Revisit the same situation as in assignment 5-3. p = 50 2q D TC = q + q 2 a. Find the consumer surplus, producer surplus, total welfare and dead weight loss under monopoly pricing. b. What is the price elasticity of demand under monopoly pricing? (Hint: Look at the formula for the Lerner Index, then plug in values for p and MC.) Eric Dunaway (WSU) EconS Lecture 24 October 26, / 47