1 Competitive Industry in the Short Run

2 operating rule case 1 $/unit Q or units MC AC AVCb c The firm is a price taker - say it takes P If firm operatesif it shuts down TR = a + b + cTR = 0 TC = b + cTC = TFC = b profit = aprofit = -b. PMR a Q1 This firm should operate where MR = MC and make a positive profit

3 Profit I copied the slide form a previous set of notes. Recall we said the firm should produce the Q where MR = MC and have profit = (P – AC)Q. Well PROFIT = TR – TC = P(Q) – TC(Q/Q) = (P – (TC/Q))Q = (P – AC)Q. At the Q in the graph on the previous screen rectangle a has area (P – AC)Q. This is the profit amount.

4 We said the short run is the period of time in which at least one input is fixed. In the industry this means the number of firms is also fixed – firms outside the industry also can not get more of some input and since they are not in the industry they can not join it in the short run. Since each firm’s supply curve is its MC curve above the AVC, the industry supply is the sum of each firm’s MC. We call the industry supply the horizontal sum of each firms supply because in the graph we sum the q’s of each firm at each price. Let’s see this on the next screen.

5 Firm 1 Firm 2 P Q Add firm 1 onto firm 2 Here we just have two firms. If more, follow the same principle. Many times we just show a smooth upward sloping curve just to show the basic idea.

6 Perfect Competition in Math Terms

7 Say you have a competitive market where the demand for consumers has been added up to be Qd = 6000/9 – (50/9)P. Also say there are 50 identical firms, where each has the total cost TC = Q + Q 2. The marginal cost for each firm would be MC = Q. We know that firms that maximize profit produce the level of output where MR = MC (as long as P>=AVC). For a competitive firm P = MR, so MR = MC means P = Q, or Q = (P – 10)/2 =.5P – 5 for each firm.

8 We know the supply curve in the competitive industry is basically the summation of the MC of each firm in the industry. For one firm we have in our example P = Q. To add across all 50 firms we re-express MC as Q =.5P – (10/2). Now we add all 50 firms together: Q =.5P – (10/2) Q =.5P – (10/2)(if firms are not identical, follow this … same basic process.) Q =.5P – (10/2) Qs = 25P – 250 or P = 1/25Q + 10 The supply curve

9 Note the supply curve, Qs, adds up the supply curve of each firm..5P50 times is 25P and (10/2) 50 times is 250. So for the supply curve we have Qs = 25P – 250. The market price and quantity traded are determined where Qs = Qd, so we have 25P – 250 = 6000/9 – (50/9)P, or (225/9)P + (50/9)P = 6000/ /9, or (275/9)P = 8250/9, or P = 8250/275 = 30. Plug P = 30 into either Qd or Qs to get the quantity traded in the market. In Qs we have 25(30) – 250 = 500.

10 Since the market price is 30, each firm will make Q= (P – 10)/2 = (30-10)/2 = 10. The profit for each firm TR – TC. TR for a firm is P times Q, or PQ. TR = 30(10) = 300. TC = Q + Q 2 for each firm in this example. So, TC = (10) = 300. Profit = 300 – 300 = 0.

11 P D1S1ATC1 MC1 P=MR1 P1 =30 Q1=500Q1=10 Q q MarketFirm

12 D S P Q Industry or marketfirm P=D =MR = AR MC = S Here we have the industry P and Q where S=D and the firm output level q where MR = MC, or we could say P = MC since P=MR. (presumably the firms MC are above AVC, so we have profit max positions.)

13 Change in fixed cost A change in the fixed cost for firms in the industry will not change the industry at all in the short run. In the short run a change in fixed cost will just affect the amount of profit for the firm. But it can not drive the firm out since the MC is above the AVC. Variable costs are covered and some amount of the fixed cost has to be covered. In the long run we could have a very different story. But, let’s look at an analogy to get the short run story. The fish tank analogy. Look at the next several slides quickly, to simulate a fish tank being filled with water.

14 Hose and water going into tank Water level

15 Hose and water going into tank Water level

16 Hose and water going into tank Water level

17 Hose and water going into tank Water level

18 Hose and water going into tank Water level Wow, this is wild!

19 $/unit Q or units MC AC AVC d P MR Q1 e f Here is where we get the pay – off from the fish bowl analogy. Given the price, the firm looks at its revenue as e and f filling the tank as shown by d+e+f. Have the water fill in from the bottom up. Since the revenue covers the TVC – area f - and some of the TFC – area d + e – it is better to operate. A change in the fixed cost doesn’t change the fact that TVC would be covered and some of the fixed cost. If the firm shut down it would have no variable cost and all the fixed cost to pay with no revenue. By producing, the revenue covers all the variable and some of the fixed. So the firm loses less. Remember, see the revenue fill area f and e from the bottom up.

20 D S P Q Industry or marketfirm P=D =MR = AR MC = S Say variable costs rise in such a way that MC for firms rises. Here I show the MC curve shift left. The industry supply will shift left because the industry is simply the sum of all the firms. Market price will rise and output will fall. With a higher market price the firm demand line = price line will rise. Where I show the industry supply, the price means the firm would have the same level of output as before the change. Can this be?

21 The output for all firms in the industry can not be the same if the output in the industry is lower. On average, output has to fall at the firm level. If the firm shown had had slightly steeper curves the output for the firm would have fallen. So, we see a special case in my graph. Demand in market rises If demand in the market rises we would see a higher price and a greater quantity coming out of the market. Each firm would have more output at the higher price. Next, we want to explore the cost of making the industry output. The conclusion is that firms as a group will make the industry output the cheapest that it can be made. Let’s turn to this next.

22 Refresher – What information the marginal cost curve contains. $ Q MC At a quantity, the height of the MC curve tells us how much is added to cost when that unit is added. The height would also tell us how much cost would go down if that unit was not produced.

23 Market – scale is larger than each firm Firm 1Firm 2 Q Q Q $$ $ D S MC1 MC2 Q1 Q2 P The output made in the market is made with the lowest cost. Let’s see how. Normally each firm makes Q where MR = MC and since P = MR, P = MC. Say I have power to make firms change – say I make firm 1 make 1 more unit and to keep total output the same I make firm 2 make 1 less. Firm 1’s cost goes up by price + something. Firm 2’s cost goes down by the price. So price + something minus price = something. Making firms change from what they want makes cost of market output rise.

24 Producer Surplus When producers sell products in the market they may receive more than the amount they needed to receive to supply a unit – they receive producer surplus.

25 producer surplus Recall that the supply curve shows various prices and associated quantities producers would make available for sale. The amount they need to receive to induce them to make available for sale units of a product are located on the supply curve. In fact the law of supply is an expression that they need to receive more in order to make available additional units. The amount actually received is market determined.

26 need to receive P S Q a b c d e P2 P1 1 2 Notice at P1 that only 1 unit is supplied. P1 is not enough of an amount to have the 2 nd unit supplied. To get 2 units supplied, P2 is required.

27 need to receive On the previous slide we see that to get 1 unit supplied P1 was need. P1 times 1 = P1 and is the area of the rectangle made up of C and D. This is the amount needed to supply the first unit. If we ignore area c we could say the area under the supply up to 1 unit is the amount needed to get that unit supplied. You see the area under the curve is an under-estimate of the amount needed but it makes life easy in terms of a visual look. Similarly area b + e = P2, the amount needed to have the second unit supplied. If you ignore b we have just the area under the curve. The area under the supply curve out to a quantity is the amount needed to supply those units.

Producer surplus P Q A B Area A =.5(300)(10 - 4) =900 Area A + B = 10(300) = 3000 Area B = A + B – A = 2100 Producers actually receive A + B = 3000, but only needed B = 2100, so the producer surplus is A = With S & D we get P = 10 and Q = 300

29 producer surplus What do producers do with the surplus received? They may use it to pay off some expenses or it could be a part of profit.

30 A PART OF THE INVISIBLE HAND Do you see it?

31 There is a story in economics that competitive market outcomes are efficient. Efficiency means two things really. What we make we have to make it as cheaply as possible. Plus we should make the things that people want the most. What are some things we know? The market supply is the supply from all firms in the market added up. The market demand curve is the demand from each consumer added up. The price and quantity traded are determined in the market. Individual firms and individual buyers have no control over the price. The firms and individuals are price takers.

32 P Q ABCABC P1 Q1 D S

33 On the previous slide we see that consumer surplus plus producer surplus equals the area A + B, and this is the result of the market equilibrium P1 and Q1. Inside your own head can you tell if you are willing to pay more for good x over good y? I would say you can because you can determine what you like! As you compare two people can you tell who is willing to pay more for good x? This is harder, but we think the demand curve orders units in such a way that the first unit is demanded by the person who values it most in terms of their willingness to pay for it. The market price cuts off people who value the good less than those who value it more and thus the units of the good produced go to the people who value it most.

34 Think about sellers in the market. They want to make profit, where profit equals revenue minus cost. Can you tell between producers which can make units cheaper? It is hard but we think the supply curve orders units so that the first unit supplied comes from the lowest cost producer. The market cuts off suppliers who produce the good at too high a cost compared to those who produce at lower cost. So, the market is efficient because goods go to those who value them most and are produced by the producers who can do it cheapest.

35 P Q ABCABC P1 Q1 D S e h qlessquamore g

36 Another way to think about efficiency is the total amount of consumer and producer surplus together. The total surplus is less when output is less than the market outcome at Q1, like at qless. Here we would see surplus fall by area e + h. If output is higher than Q1, like at quamore, then we force on the market units of the good that costs more to make than people are willing to pay to get. This is not good. Summary A competitive market is most efficient because we get the most total surplus out of it.