# EconS Perfect Competition and Monopoly

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1 EconS Perfect Competition and Monopoly Eric Dunaway Washington State University Industrial Organization Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 47

2 Introduction Today we ll review the structure of the perfectly competitive and monopoly markets. We ll also dust o how welfare calculations are done. Eric Dunaway (WSU) EconS 425 Industrial Organization 2 / 47

3 Supply and Demand Consider a setting where there are n identical rms. Each of these rms faces an individual demand function where for any given price p, consumers will demand a corresponding quantity from rm i, q i, of that good or service. As a function, q D i = q D (p) Under normal conditions (i.e., not a Gi en good), as the price of the good or service increases, the quantity demanded decreases. Thus, dq D i qp < 0 Eric Dunaway (WSU) EconS 425 Industrial Organization 3 / 47

4 Supply and Demand We can add up all of these individual rms to form the aggregate demand curve Q D n = qi D i=1 where the aggregate quantity also decreases with increases in the market price. Remember that we have to add demand curves together horizontally. By that, I mean that only quantities can be added together (Honestly, it would make no sense to add prices together). Eric Dunaway (WSU) EconS 425 Industrial Organization 4 / 47

5 Supply and Demand A quick example. Consider two identical rms with the following demand functions: q 1 = 10 2p q 2 = 10 2p We can aggregate these two demand functions together to obtain Q D = q 1 + q 2 = 20 4p Note: It s not this easy when the rms are not identical; you have to take rm participation into question. Eric Dunaway (WSU) EconS 425 Industrial Organization 5 / 47

6 Supply and Demand A lot of the time, it s useful to refer to the inverse demand function, which is obtained by solving the demand function for price, p. This is primarily a mathematical convenience. In reality, rms choose prices, rather than quantities. In our above aggregate demand example, Q D = 20 4p we solve for price to obtain the inverse aggregate demand, p = QD Eric Dunaway (WSU) EconS 425 Industrial Organization 6 / 47

7 Supply and Demand On the other end of the market, each of the n rms has an individual supply curve, where for every value that the market price can take, there is a quantity that rm i will supply to the market, q i q S i = q S (p) Contrary to the demand curve, under all conditions, an increase in price causes rm i to supply more of their good or service to the market. dq S i dp > 0 Eric Dunaway (WSU) EconS 425 Industrial Organization 7 / 47

8 Supply and Demand Likewise, we can add all of the individual rm supply curves together to obtain the aggregate, or market supply curve, Q S = n qi S i=1 Remember that the supply curve is identical to the marginal cost curve, as long as the price is above the rm s average variable cost. If price is below the average variable cost, the rm would prefer to not produce at all. Eric Dunaway (WSU) EconS 425 Industrial Organization 8 / 47

9 Supply and Demand p Q Eric Dunaway (WSU) EconS 425 Industrial Organization 9 / 47

10 Supply and Demand p Q D Q Eric Dunaway (WSU) EconS 425 Industrial Organization 10 / 47

11 Supply and Demand p Q D Q S Q Eric Dunaway (WSU) EconS 425 Industrial Organization 11 / 47

12 Perfectly Competitive Market Lets move on to the perfectly competitive market. Recall the four main assumptions that de ne the perfectly competitive market: Large number of buyers and sellers. Firms produce identical products. Everyone has perfect information. Firms can easily enter and exit the market. Eric Dunaway (WSU) EconS 425 Industrial Organization 12 / 47

13 Perfectly Competitive Market With regard to the large number of buyers and sellers, this implies that the number of rms, n, has to be quite large. In fact, n has to be large enough to assume that any individual rm s output decision, q i, does not have a noticeable on the total market output, Q. Mathematically, dq dq i 0 In other words, in a perfectly competitive market, one rm s decisions don t in uence what any other rm chooses to do in that market. Every rm is able to act individually. Eric Dunaway (WSU) EconS 425 Industrial Organization 13 / 47

14 Perfectly Competitive Market In our perfectly competitive market, each rm seeks to maximize their pro ts, which is de ned as total revenue minus total cost max TR TC Mathematically, it doesn t whether price or quantity is chosen as the dependent variable, it will work out the same. It s almost always simpler to use quantity. In a practical setting, price is used. If price is chosen, use the aggregate demand function. If quantity is chosen, use the inverse aggregate demand function. Why the aggregate? All rms face the market price. Eric Dunaway (WSU) EconS 425 Industrial Organization 14 / 47

15 Perfectly Competitive Market Subtituting for total revenue and total cost, max q i p(q)q {z } i TR c(q i ) {z } TC where p(q) is the inverse aggregate demand function, and c(q i ) is the total cost faced by rm i. Calculating a rst-order condition, p 0 (Q) dq dq i + p(q) {z } MR c 0 (q i ) = 0 {z } MC Eric Dunaway (WSU) EconS 425 Industrial Organization 15 / 47

16 Perfectly Competitive Market p 0 (Q) dq dq i + p(q) c 0 (q i ) = 0 This is where our assumption that dq dq i 0 become important. We can cancel out the rst term above in order to obtain Or, rearranging p(q) c 0 (q i ) = 0 p(q) = c 0 (q i ) In words, this is the classic result from the perfectly competitive market: price equals marginal cost. Eric Dunaway (WSU) EconS 425 Industrial Organization 16 / 47

17 Perfectly Competitive Market p(q) = c 0 (q i ) Graphically, this is fairly easy to solve. The left-hand side of this equation can be replaced with the inverse market demand function. The right-hand side of this equation is simply the supply curve, as mentioned above. Eric Dunaway (WSU) EconS 425 Industrial Organization 17 / 47

18 Perfectly Competitive Market Example Consider a rm in a perfectly competitive market that faces the following inverse market demand curve p = 100 2Q and the following competitive supply curve p = 10 + Q Find the equilibrium price and quantity for this rm. Eric Dunaway (WSU) EconS 425 Industrial Organization 18 / 47

19 Perfectly Competitive Market Example p = 100 2Q p = 10 + Q First, we need to nd the marginal cost function, which is simply the supply curve, MC = 10 + Q Then, just set the inverse demand function (price) equal to the marginal cost p = MC 100 2Q = 10 + Q Eric Dunaway (WSU) EconS 425 Industrial Organization 19 / 47

20 Perfectly Competitive Market Example 100 2Q = 10 + Q Solving this expression for Collecting terms, 3Q = 90 Q = 30 We can nd the market price by simply plugging this value back into the inverse market demand curve p = 100 2Q = 100 2(30) = 40 Eric Dunaway (WSU) EconS 425 Industrial Organization 20 / 47

21 Perfectly Competitive Market Example 100 p Q D QS Q Eric Dunaway (WSU) EconS 425 Industrial Organization 21 / 47

22 Perfectly Competitive Market Example 100 p Q D QS Q Eric Dunaway (WSU) EconS 425 Industrial Organization 22 / 47

23 Monopoly Now let s look at monopoly, which nds itself on the opposite end of the competition spectrum. Monopoly has the following assumptions: One seller, and a large number of buyers. Firms produce identical products. Everyone has perfect information. No rms can enter the market. Eric Dunaway (WSU) EconS 425 Industrial Organization 23 / 47

24 Monopoly Since there is only one rm in this case, n = 1 and Q = q i, i.e., the monopolist s output level is the same as the market output level. Furthermore, we can di erentiate Q = q i to obtain dq dq i = 1 While the monopolist gets the bene t of setting its own price (market power), it also has to take the consequence of its price into consideration, as a higher price will lead to a lower quantity demanded by its consumers. Eric Dunaway (WSU) EconS 425 Industrial Organization 24 / 47

25 Monopoly Returning to our rst-order condition from the pro t maximization problem, We can use Q = q i and dq dq i p 0 (Q) dq dq i + p(q) {z } MR c 0 (q i ) = 0 {z } MC = 1 to rewrite this as p 0 (Q) + p(q) {z } MR c 0 (Q) = 0 {z } MC and rearranging, we obtain the classic equilibrium de nition for a monopolist: p 0 (Q) + p(q) = c 0 (Q) {z } {z } MR MC or more generally, marginal revenue equals marginal cost. Eric Dunaway (WSU) EconS 425 Industrial Organization 25 / 47

26 Monopoly p 0 (Q) + p(q) = c 0 (Q) There is also a neat math de nition in this statement. Let s rearrange it a bit. p(q) = c 0 (Q) p 0 (Q) Remember that p 0 (Q) < 0. Since as price goes up, quantity demanded goes down (we can also say that as quantity demanded goes up, price goes down). This means that for a monopolist, price has to be greater that marginal cost, because the right-hand side of this equation must always be greater than simply marginal cost. Eric Dunaway (WSU) EconS 425 Industrial Organization 26 / 47

27 Monopoly Example Let s look at the same example as before, with the following inverse market supply and demand curves. p = 100 2Q p = 10 + Q Now, we ll solve it from the perspective of a monopolist. Eric Dunaway (WSU) EconS 425 Industrial Organization 27 / 47

28 Monopoly Example p = 100 2Q p = 10 + Q First, we need to nd the marginal revenue, which we obtain from the total revenue, TR = pq = (100 2Q)Q = 100Q 2Q 2 Next, we di erentiate with respect to Q to obtain the marginal revenue MR = 100 4Q And set it equal to marginal cost (the supply curve) MR = MC 100 4Q = 10 + Q Eric Dunaway (WSU) EconS 425 Industrial Organization 28 / 47

29 Monopoly Example 100 4Q = 10 + Q Rearranging, and solving for Q gives the monopolist s equilibrium output level 5Q = 90 Q = 18 And to nd the equilibrium price, we plug the equilibrium quantity into the demand function (Be careful not to plug it into marginal revenue!) p = 100 2Q = 100 2(18) = 64 Eric Dunaway (WSU) EconS 425 Industrial Organization 29 / 47

30 Monopoly Example 100 p Q D QS Q Eric Dunaway (WSU) EconS 425 Industrial Organization 30 / 47

31 Monopoly Example 100 p Q D QS 10 MR 50 Q Eric Dunaway (WSU) EconS 425 Industrial Organization 31 / 47

32 Monopoly Example 100 p Q D QS MR 50 Q Eric Dunaway (WSU) EconS 425 Industrial Organization 32 / 47

33 Monopoly Example 100 p Q D QS MR 50 Q Eric Dunaway (WSU) EconS 425 Industrial Organization 33 / 47

34 Comparing PC and Monopoly Let s check what we predicted before about the relationship between perfect competition and monopoly. Perfect Competition Monopoly p Q As predicted, the monopoly yields a higher price than perfect competition while producing a less. Eric Dunaway (WSU) EconS 425 Industrial Organization 34 / 47

35 Comparing PC and Monopoly 100 p Q D QS 64 Monopoly 40 Perfect Competition MR Q Eric Dunaway (WSU) EconS 425 Industrial Organization 35 / 47

36 Welfare What about welfare levels? Let s brush up on those, too. Recall that the di erence between what a consumer was willing to pay for a good or service and the price they actually pay is known as consumer surplus. Likewise, the di erence between what a producer receives and what they were willing to sell a good for is known as producer surplus. Adding them up, we get the total welfare. Eric Dunaway (WSU) EconS 425 Industrial Organization 36 / 47

37 Welfare p Q D Q S Consumer Surplus Producer Surplus Q Eric Dunaway (WSU) EconS 425 Industrial Organization 37 / 47

38 Welfare We can obtain the consumer surplus by integrating the di erence between the inverse market demand function and the equilibrium price from zero to the equilibrium quantity, i.e., CS = Z Q 0 h p D (Q) p i dq Similarly, we can obtain the producer surplus by integrating the di erence between the equilibrium price and the inverse market supply functon from zero to the equilibrium quantity, PS = Z Q 0 h p i p S (Q) dq Or, if your instructor is feeling nice and gives you linear supply and demand functions, just use triangle and trapezoid formulas. Returning to our example, Eric Dunaway (WSU) EconS 425 Industrial Organization 38 / 47

39 Welfare 100 p Q D QS 40 CS PS Q Eric Dunaway (WSU) EconS 425 Industrial Organization 39 / 47

40 Welfare Starting with consumer surplus, we can use a triangle formula, CS = 1 (100 40)(30) = And doing the same thing with producer surplus, PS = 1 (40 10)(30) = Adding them together gives us the total welfare level, W = CS + PS = 1350 Eric Dunaway (WSU) EconS 425 Industrial Organization 40 / 47

41 Welfare 100 p Q D QS 64 CS PS MR 50 Q Eric Dunaway (WSU) EconS 425 Industrial Organization 41 / 47

42 Welfare Again, calculating the consumer surplus, CS = 1 (100 64)(18) = For producer surplus, we actually have a trapezoid, so we have to make sure we use the correct formula, PS = 1 ( )(18) = Lastly, we calculate the welfare level of the monopoly, W = CS + PS = 1134 Eric Dunaway (WSU) EconS 425 Industrial Organization 42 / 47

43 Welfare Comparing our results, Perfect Competition Monopoly CS PS W We can see that consumer surplus falls, producer surplus rises, and total welfare falls under monopoly. In fact, the di erence between the perfectly competitive and monopoly levels of welfare is known as the dead weight loss. This is the amount of economic activity (measured in dollars) that is being lost due to a distortion in the market. Eric Dunaway (WSU) EconS 425 Industrial Organization 43 / 47

44 Welfare 100 p Q D QS 64 CS DWL PS MR 50 Q Eric Dunaway (WSU) EconS 425 Industrial Organization 44 / 47

45 Summary In order to understand imperfect competition, we need to have a baseline to compare our results to (perfect competition) Monopoly represents the opposite end of the competitive spectrum from perfect competition, and is a signi cant source of market power. Monopolists produce less, charge more, and create market distortions. Eric Dunaway (WSU) EconS 425 Industrial Organization 45 / 47

46 Next Time Intertemporal considerations. How patient are rms and consumers? What happens when we add time as a factor to our models? Reading: Section 2.2 Eric Dunaway (WSU) EconS 425 Industrial Organization 46 / 47

47 Assignment 1-2 Consider a market that faces the following inverse demand and total cost curves, P = 500 Q TC = Q + Q 2 1. Calculate the equilibrium price and quantity if this market is perfectly competitive. 2. Calculate the equilibrium price and quantity if this market is monopolized. Eric Dunaway (WSU) EconS 425 Industrial Organization 47 / 47

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