EconS Monopoly - Part 1

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1 EconS Monopoly - Part 1 Eric Dunaway Washington State University October 23, 2015 Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

2 Introduction For the rest of the semester, we re going to look at additional topics of microeconomic theory. Today, we will look at how monopoly works. This is the case where there is only one seller of a product for a market. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

3 Monopoly What is a monopoly? At its simplest form, one seller, many buyers. If we compare this to perfect competition, this breaks our rst assumption that there are many buyers and many sellers. This allows the monopolist to attain market power. E ectively, the monopolist can choose either the market price or the market quantity, with the other taking shape from the demand function. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

4 Monopoly Aren t monopolies illegal? Yes and no. In the US, engaging in anticompetitive practices to drive out competitors is highly illegal. Example: ALCOA in the early 20th century. However, some market work better as a monopoly, like public utilities. In this case, the government will regulate the monopoly. Also, patents grant monopoly power to rms who produce new products for a limited time, allowing them to recoup their research costs. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

5 Patents A great place where we see patent driven monopolies is in the pharmaceutical industry. A company will develop a new drug and patent it, allowing them to be the sole producer for 20 years. During this time, the price is quite high. After the patent expires, competitors can now start making and selling the same drugs. This is where the generic drugs come from. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

6 Monopoly Let s look at the other causes for monopoly. Without government intervention, monopoly will emerge if one rm can operate at a signi cantly lower cost than its competitors. They can match their prices to their costs, and it will drive their competitors out. Microsoft vs. Netscape in the mid 1990 s. This also happens when one rm controls all of a scarce resource. ALCOA. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

7 Natural Monopoly An extreme example of this is natural monopoly. We see this in public utilities. This happens when it is cheaper for one rm to produce all of the quantity than it is for many rms to individually produce the same quantity. Mathematically, where Q = q 1 + q q n. C (Q) < C (q 1 ) + C (q 2 ) C (q n ) We can see the case for natural monopoly in certain long run average cost functions. If a market has economies of scale (downward sloping long run average cost curve) for all levels of output, a natural monopoly will form. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

8 Natural Monopoly C/q AC MC q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

9 Natural Monopoly At its core, a natural monopoly will develop if it is cheaper for one rm to produce the same amount as two smaller rms. The rm with the higher share of the market will beat its competitor out and take over the market. For example, it is cheaper (and more e cient) for one company to run water pipes underneath the street than two companies trying to run pipes to every home and competing against one another. This is why there is typically only one water/power/telephone company per city. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

10 Monopoly Another type of monopoly are government granted monopolies. These have no speci c cost bene ts, but the government typically either runs the rm, or auctions o the monopoly rights to a single rm. Example: US Postal Service, Cable companies. In order to do this, the government forbids entry of any other rm into the market, creating perfect barriers to entry. There goes another assumption from the perfectly competitive market! Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

11 Monopoly How do monopolists maximize their pro ts? Since we are not using perfect competition any more, we can t use p = MC. That no longer holds. We were only able to use it before because each individual rm faced a horizontal demand curve. The could sell as much as they wanted to at the given market price. A monopolist faces the market demand curve, and the quantity they sell will be directly related to the price they choose. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

12 Marginal Revenue Thus, we need to go back to our original, very important de nition. MR = MC Remember that we got this last week when we gured out that pro t maximization occurs when marginal pro ts equal zero. How do we derive the marginal revenue curve? For linear demand curves, we can do it graphically. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

13 Marginal Revenue p D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

14 Marginal Revenue p D MR Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

15 Marginal Revenue The marginal revenue curve always starts at the same point as the demand curve on the vertical axis. It has double the slope as the demand curve, however, and crosses the horizontal axis at the midpoint between the origin and the horizontal intercept of the demand curve. This relationship should make more sense when we derive it mathematically. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

16 Marginal Revenue Remember from before that we can express total revenue as the price of a good times its quantity TR = pq The monopolist can only choose one of these variables (it does not matter which one, the equilibrium answer will be the same) and the other will be determined by the demand function. Once we pick which which variable we are going to use, we substitute either the demand or inverse demand function for the other variable, then use the power rule with respect to our chosen variable to derive the marginal revenue. That s a long sentence. Let s look at an example to clear it up. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

17 Marginal Revenue Consider a monopolist that faces the demand curve q D = 10 2p To get the monopolist s marginal revenue curve, we start with the total revenue de nition TR = pq For simplicity, let s say the monopolist chooses its price. Then, we just substitute the demand function for q in the total revenue equation. TR = p(10 2p) Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

18 Marginal Revenue TR = p(10 2p) From here, we distribute the price through TR = 10p 2p 2 and then we apply the power rule with respect to p to get the marginal revenue MR = 10 4p Notice that it has the same intercept as its demand counterpart, but has double the slope. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

19 Marginal Revenue What if the rm chose the quantity instead? Then we just substitute in the inverse demand function p = 5 Our total revenue function becomes TR = q 1 2 q q = 5q 1 2 q2 and applying the power rule with respect to q yields the marginal revenue MR = 5 q Again, notice that it has the same intercept, but double the slope. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

20 Marginal Revenue But they aren t the same. Correct. In the rst example, I calculated the marginal revenue with respect to price, or how much more revenue the monopolist receives by increasing its price by 1 unit. In the second example, I calculated the marginal revenue with respect to quantity, or how much more revenue the monopolist receives by increasing its output by 1 unit. As long as we calculate our marginal cost with respect the same variable, the equilibrium answers will work out. For the most part, we will use quantity, because it s easier for marginal cost. Just be careful with your math. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

21 Marginal Revenue p 5 D 10 Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

22 Marginal Revenue p 5 D MR 5 10 Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

23 Monopoly Pro ts Now that we have the marginal revenue side of the equation gured out, we just need the marginal cost in order to solve. To get the marginal cost function, we just use the same techniques that we did last week. So what will our solution look like? We need to draw the average cost functions on top of our demand and marginal revenue functions. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

24 Monopoly Pro ts p MR D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

25 Monopoly Pro ts p AC AVC MR D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

26 Monopoly Pro ts p MC AC AVC MR D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

27 Monopoly Pro ts From here, the monopolist chooses the quantity where the marginal revenue and marginal cost curves intersect, then it moves up to the demand curve to nd its price. This can be a bit confusing. In the previous gures, all of the marginals are determined with respect to quantity. Thus, they can t tell us anything about the price. The demand curve can, though, since the price will just be a function of the output quantity. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

28 Monopoly Pro ts p MC p * AC AVC Q * MR D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

29 Monopoly Pro ts As in perfect competition, we take the distance between the equilibrium price and the average cost curve, multiply it by the quantity, and that gives us the total pro ts. We could also just plug the values of p and q back into the total revenue and total cost functions and solve them mathematically. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

30 Monopoly Pro ts p * p Profits MC AC AVC Q * MR D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

31 Monopoly Pro ts Will the monopolist want to produce? This is also just like the perfect competition counterpart. As long as the price is above the average variable cost, the monopolist wants to produce, even if it is taking a loss. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

32 Monopoly Pro ts How does the monopoly equilibrium compare to a perfectly competitive equilibrium? We can see this on our gure, too. Remember that the marginal cost curve is the same thing as the supply curve when it is above the average variable cost. Under perfect competition, we will price where p = MC, or supply equals demand. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

33 Monopoly Pro ts p MC (S ) p M AC AVC Q M MR D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

34 Monopoly Pro ts p MC (S ) AC AVC p M p C MR Q M Q C D Q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

35 Monopoly Pro ts This leads to a central intuition of the monopoly equilibrium. In equilibrium, the monopolist will produce less and charge more than it would under perfect competition. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

36 Example A monopolist faces an inverse demand curve of p = 100 q and a total cost curve of TC = q What are the equilibrium quantity, price, and pro t levels for the monopolist? Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

37 Example First, we need the marginal revenue function. Starting with total revenue TR = pq we can substitute the inverse demand funciton in for p, yielding TR = (100 q)q = 100q q 2 Applying the power rule with respect to q, we get our marginal revenue MR = 100 2q Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

38 Example Next, we need the marginal cost function. Starting with total cost TC = q we apply the power rule with respect to q to get our marginal cost function MC = 5 This actually implies that the marginal cost (supply) curve is at! Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

39 Example p 100 D MR 5 50 MC (S ) Q 100 Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

40 Example Now, we set marginal revenue equal to marginal cost to nd our equilibrium quantity, MR = MC 100 2q = 5 2q = 95 q = 47.5 We can plug this value back in to the inverse demand function to nd our equilibrium price, p = 100 q = = 52.5 Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

41 Example p 100 D MR MC (S ) Q 100 Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

42 Example Lastly, we want to nd our equilibrium pro t level. We can do this by rst nding our total revenue and total cost, TR = p q = 52.5(47.5) = TC = q = (47.5) = and our equilibrium pro t level is just the di erence between the two π = TR TC = = Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

43 Example How would this compare with the equilibrium price, quantity and pro ts if the monopolist acted as if he were competing in a perfectly competitive market? This would be a simple supply and demand problem. Recall that the supply curve is just the marginal cost curve when we are above average variable costs. In this case, our supply curve is completely at at p = 5 which actually makes this problem pretty easy to solve. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

44 Example From the inverse demand function, p = 100 q we can plug in p = 5 from the inverse supply function to obtain 5 = 100 q Adding q to both sides and subtracting 5 from both sides gives us our equilibrium quantity q = 95 Thus, our equilibrium price and quantity are p = 5 q = 95 which aligns with where supply and demand intersect on our gure. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

45 Example p 100 D MR 5 MC (S ) Q 95 Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

46 Example The monopolist s total revenue and total costs under perfect competition are yielding total pro ts of TR = p q = 5(95) = 475 TC = q = (95) = 485 π = TR TC = = 10 Ouch, the monopolist actually doesn t make any money under perfect competition due to the xed cost! Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

47 Example Let s compare the results for the monopolist when he competes under both a monopoly setting and a perfect competition setting. Monopoly Perfect Competition p q π As we can see, the results are quite di erent. There isn t usually this much of a di erence. The at supply curve muddles things up a bit. What s important to see is that our results from earlier still hold. The monopoly price and pro ts are higher than their perfect competition counterparts, while the monopoly quantity is lower than its perfect competition counterpart. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

48 Summary Monopoly occurs when one rm is able to act as the sole provider for the market. Monopolistic equilibrium will have a higher price and a lower quantity than a perfectly competitive equilibrium. Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

49 Preview for Monday Part 2 of Monopoly Welfare E ects! How much dead weight loss does a monopolist create? Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

50 Assignment 5-3 (1 of 1) 1. Consider a monopolist that operates under the following inverse demand curve p = 50 2q D and faces total cost curve TC = q + q 2 a. What is the equilibrium quantity, price, and pro t level if the monopolist acted as if he were in a perfectly competitive market? b. What is the equilibrium quantity, price, and pro t level if the monopolist acted as if he were in a monopoly market? c. Do these results make sense? Why or why not? Eric Dunaway (WSU) EconS Lecture 23 October 23, / 50

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