ECONOMICS 103. Topic 7: Producer Theory - costs and competition revisited

Transcription

1 ECONOMICS 103 Topic 7: Producer Theory - costs and competition revisited (Supply theory details) Fixed versus variable factors; fixed versus variable costs. The long run versus the short run. Marginal and average productivity of labour (and other variable factors). Marginal costs revisited; average variable costs; average total costs; average fixed costs. Producer surplus versus profits. Short and long run competitive equilibria. 1

2 PRODUCER BEHAVIOUR We want to look in more detail at behaviour underlying supply. What do we know about supply in competitive markets? - Producers sell more of a good if MB (P) > MC of production. - Producer sell less of a good if P < MC. - Choosing to sell where P = MC maximizes PS. - Tells us that the MC curve is the S curve for a comp firm. So far, we have made assumptions about what MC curves look like. - In this topic, we want to think more about production and costs in order to understand various possibilities. - We also want to think in more detail about how the firm s time horizon is relevant for decisions making. 2

3 PRODUCER COSTS 1st step: to understand different types of costs that firm face. - These are a function of firm s decision-making time-horizon. Definitions: Short run (SR) = Period of time in which the firm cannot change the amount used of at least one input. - We call any input whose quantity cannot be changed in the SR a fixed input. - Cost of this input is called a fixed cost (FC). - Note that, by definition, FC cannot change in SR. The amount used of some inputs can be changed in the SR. - We call these inputs variable inputs. - Costs of these inputs are called variable costs (VC). Firms total costs (TC) = FC + VC. 3

4 COSTS More definitions/derivations: Long run (LR) = Period of time in all inputs can be varied. - For now, we will be focussing on SR, more on LR soon. Marginal cost: we already know this is cost of 1 more unit. - Here, we can calculate MC as follows. MC = TC/ Q =( FC+ VC)/ Q. - Since FC/ Q = 0 (by definition), we are left with: MC = VC/ Q. Various measure of average cost are also now important. Average Fixed Cost (AFC) = FC/Q. Average Variable Cost (AVC) = VC/Q. Average Total Cost () = TC/Q = AFC + AVC. 4

5 COSTS Simplifying assumptions: - We will assume only one fixed input, capital (K). Can think about K as start-up cost of setting up a business. Example: rental of a restaurant space. This cost needs to be incurred before firm can sell any output. Means fixed costs are K costs. - We will also assume only one variable input, labour (L). In order to sell any output, we have to hire L. Means variable costs are L costs. Given above definitions/assumption, we want to look at different possibilities for all shapes of costs curves. 5

6 COSTS In particular, we want to understand the story that gives rise to the cost curves illustrated below. MC AVC Best way for you to understand this story properly is by working through examples. Important: work through the example posted on webpage. Q In lecture, we will tell the general story behind these cost curves. But to understand this properly, most students need to work through at least a few numerical examples. This is one of those concepts that you need to work on outside class to fully understand. 6

7 COSTS We begin with MC. MC This MC doesn t look like earlier versions we have used. We have looked at: - Upward-sloping MC; and - Constant (horizontal) MC. Q Why might MC look like this? To understand this, we need to think about input productivity and recall the distinction between the SR and the LR. MC drawn above is for the SR, when at least one factor is fixed. 7

8 PRODUCTIVITY Productivity measures/definitions. - Total product (TP) = amount of total output a firm can produce at different level of L, taking as given the level of K. TP = Q, and is a function of L (given fixed K). - Marginal product of labour (MPL) = additional output we get from hiring an extra worker. MPL = TP/ L = Q/ L. We want to understand that MC drawn on previous slide corresponds to case where MPL: - Increases for a period when L is relatively low - But decreases when L is relatively high. 8

9 PRODUCTIVITY TP (Q) TP Note TP is upward sloping. More L, results in more Q. BUT, rate of increase is not constan Rate of increase is slope of TP. Here: - Slope is increasing for low L. - Slope is decreasing for high L. Slope is TP/ L = Q/ L = MPL. 9 L

10 PRODUCTIVITY MPL (Q) MPL L So MPL looks like this. Why? 10

11 PRODUCTIVITY MPL (Q) Crowding of fixed factor Returns to specialization MPL L At low L, we get returns to the division of labour. - Each worker can specialize more, hence productivity increases. But can only happen for a while, since K fixed. - At high L, additional workers start to crowd the fixed factor, so MPL begins to diminish. 11

12 PRODUCTIVITY MPL (Q) MPL L If MPL looks like this.. 12

13 COSTS MC Returns to specialization Crowding of fixed factor Q Then MC looks like this. If each additional worker more productive than the last, cost of additional unit of output will be lower. If each additional worker less productive than the last, cost of additional unit of output will be higher. 13

14 COSTS MC Returns to specialization Crowding of fixed factor Q So with more realistic model of production, different possibilities arise re shape of MC. In Topic 7 (and 8), we will mostly work with this u-shaped MC curve. Understand the assumptions underlying the shape. 14

15 COSTS Next we want to understand AVC. Recall that the shape of MC was derived from shape of MPL. AVC Q Turns out that the shape of AVC is derived from shape of APL. Average product of labour (MP) = average output we get from hiring a given number of workers. APL = TP/L = Q/L. 15

16 PRODUCTIVITY MPL (Q) MPL L If MPL looks like this.. 16

17 PRODUCTIVITY MPL (Q) APL MPL L Then APL looks like this. - Work through the example posted on the web page to convince yourself why this must be so. If APL looks like this. 17

18 COSTS Then AVC looks like this. APL increasing APL decreasing AVC Q 18

19 COSTS MC and AVC together. MC Note: MC passes through AVC at the minimum point of AVC. Logically, must be true. AVCMIN AVC Q Think about relationship between average and marginal variables to understand why. AVCMIN turns out to be very important, in SR. We will see that P = AVCMIN is what we call the shutdown price for the firm. 19

20 COSTS Finally, we need to understand. will have similar u-shape to AVC, though for slightly different reasons. Q Work through example posted on web page to fully understand. 20

21 COSTS Recall that = AFC + AVC. AFC & AVC AFC & AVC. But at high Q, AFC is small. Q Work through example posted on web page to fully understand. 21

22 COSTS MC and together. MIN MC Note: MC passes through at the minimum point of AVC. Similar logic as for MC/ AVC relationship. Q MIN also turn out to be very important, but more relevant of the LR. We will see that P = MIN is what we call the breakeven price for the firm. 22

23 COSTS AVC and together. At low Q, AFC is large. At high Q, AFC is small. = AFC + AVC. AVC So - AVC = AFC. QL QH Q As Q increases, FC are spread over more units of output, so AFC decreases. 23

24 COSTS Calculate FC. FC = AFC Q. And FC don t change. AVC QL QH Q 24

25 COSTS Calculate FC. So FC at QL = blue rectangle. AVC QL QH Q 25

26 COSTS Calculate FC. Logically, this must be equal to FC at QH. AVC QL QH Q 26

27 COSTS Putting it altogether. MC AVC We now have a story for this more complicated representation of firm costs. Q Not THAT complicated though, once you work through some examples. 27

28 COSTS AND COMPETITIVE FIRMS These cost curves are not unique to perfectly competitive firms. - We can (and will) use them to think about non-comp markets. But for now, recall we are looking at price-taking firms. We already know how such firms optimally choose Q. - Marginal analysis (just like in Topic 1). Rule: produce an extra Q if MB > MC. Stop when MB = MC. - Here, MB = P, which we will also call Marginal Revenue (MR). - Key: for competitive firms MR = P. We know this rule maximizes PS already. Now we want to see that it also maximizes profits (Π), and understand relationship between PS & Π. 28

29 PROFIT V PRODUCER SURPLUS Recall definition of producer surplus: - PS = (P Q) minus minimum amount need to supply the quantity in question. In this context, that minimum amount need is simply VC. - Firm better be able to cover at least its VC. So we can now express producer surplus as: - PS = TR - VC = (P Q) - (AVC Q) = (P - AVC) Q. Definition of profits (Π): - Π = TR - TC = (P Q) - ( Q) = (P - ) Q. 29

30 PROFIT V PRODUCER SURPLUS PS = TR - VC = (P - AVC) Q. Π = TR - TC = (P - ) Q. The only difference between Π & PS is the difference between TC and VC, which is just FC. - That is, we have PS - Π = FC. - PS is larger than Π, since in calculating PS we do not subtract FC, while in calculating Π we do. Recall that we were often interested in calculating changes in PS. Because - by definition - FC do not change, we have: - PS = Π. So our measure of the change in firm welfare maps well into our understanding that real-world firms are motivated by profit. Next step is to understand this all, diagrammatically. 30

31 OPTIMAL CHOICE Competitive firm takes P = MR as given. MC AVC P = MR Chooses q to max Π, taking P as given. q Switching to lower-case q to denote an individual firm s output. We will use upper-case Q to denote market (industry) output. 31

32 OPTIMAL CHOICE Just doing marginal analysis, as always. MC AVC P = MR So optimal choice here is q*. q * q We want to calculate both Π & PS, diagrammatically. 32

33 OPTIMAL CHOICE Recall Π = TR - TC = (P - ) q. MC P (q * ) AVC P = MR P - (q * ) q * q So Π = blue rectangle. 33

34 OPTIMAL CHOICE Recall PS = TR - VC = (P - AVC) q. MC AVC(q * ) AVC P = MR So PS = purple rectangle. q * q 34

35 OPTIMAL CHOICE Recall PS - Π = FC = ( - AVC) q. MC (q * ) AVC(q * ) AVC P = MR So FC = orange rectangle. q * q Straightforward, once you ve gone over it a few times. Labs this week are designed to reinforce this material. 35

36 OPTIMAL CHOICE In previous example, P > so Π > 0. Important to understand that firms may actually produce q > 0 in the short run, even if Π < 0. To understand, recall that the firm is on the hook for FC in the SR, no matter what. - That is, if firm shuts down (produces q = 0) it will lose FC. - Given q = 0, Π = - FC. But as long as P > AVC, firm makes PS > 0. - Revenues are more than enough to cover VC, so firm can at least partially offset some of its FC. Means that firm will produce q > 0 in short run if P <, as long as P > AVC. 36

37 OPTIMAL CHOICE Suppose now P is as shown below. MC P = MR AVC P lies everywhere below. No way the firm can make Π > 0. q 37

38 OPTIMAL CHOICE Suppose now P is as shown below. MC AVC P = MR Suppose it produces where MR = MC (q * ). q * q 38

39 OPTIMAL CHOICE Π = (P - ) q, which is negative here. MC (q * ) AVC P = MR Red rectangle represents losses. q * q What if firm produced q = 0 instead? 39

40 OPTIMAL CHOICE Π = - FC if q = 0. (q * ) AVC(q * ) MC P = MR AVC Larger loss incurred by shutting down (q = 0) than if q = q *. q * q Better to operate at loss, in the short run. In the long run (when firm is no longer on the hook for FC), it will want to stop operating. We call that LR decision exit (more on this shortly). 40

41 OPTIMAL CHOICE Allows us to identify different ranges of prices. MC AVC P = MR If P >, Π > 0, and firm is fine in SR and LR. q 41

42 OPTIMAL CHOICE Allows us to identify different ranges of prices. MC AVC P = MR If > P > AVC, then we have: - Π < 0 & PS > 0. q Firm will continue to operate in SR but exit in LR. 42

43 OPTIMAL CHOICE Allows us to identify different ranges of prices. MC If > AVC > PS, then we have: - Π < 0 & PS < 0, if q > 0. AVC P = MR q Firm can t even generate enough revenue to cover its VC. Firm will shut down in SR and exit in LR. 43

44 OPTIMAL CHOICE From this we can see the following; MC MIN AVC AVCMIN q P = MIN is the break even price for the firm. P = AVCMIN is the shut down price for the firm. 44

45 Each competitive firm takes price as given, where P is determined at industry/market level. We want to put all this together to think about two different concepts of equilibrium, in this context. We will differentiate between SR and LR equilibra. Recall that in the SR, capital is fixed. - Means number of firms in an industry is fixed. In LR capital is not fixed: it is free to move across industries. - What makes capital move? Profits. INDUSTRY (MARKET) LEVEL ANALYSIS In particular, if Π > 0 in any industry, then in the LR there will be entry into that industry. 45

46 INDUSTRY (MARKET) LEVEL ANALYSIS In particular, if: - Π > 0 in any industry, then in the LR there will be entry into that industry. Entry results in an increase in market supply. Increased supply lowers P, reducing Π in that industry. - Π < 0 in any industry, then in the LR there will be exit from that industry. Exit results in a decrease in market supply. Decreased supply increases P, increasing Π in industry. Tells us that in the long run, free entry and exit will ensure that Π = 0 in competitive markets. - Make sure you read text to understand that Π = 0 does not mean no firms make money! 46

47 SR V LR EQUILIBRIA Means we have slightly different conditions for SR versus LR equilibria in competitive market. Short run equilibrium: - Given P, each firm is maximizing profits: So MR = MC for each firm. - P is such that Q S = Q D at the market/industry level. Long run equilibrium: - Given P, each firm is maximizing profits: So MR = MC for each firm. - P is such that Q S = Q D at the market/industry level. - Entry and exit assure that Π = 0 for each firm. So P =, in LR. 47

48 SR V LR One firm in competitive industry Competitive market P E 1 E1 MC AVC P E 1 E1 SRS1 D Consider single firm in competitive industry illustrated here. P E 1 is determined at market level. q1 Each firm in industry chooses to produce q1. q We want to understand that E1 is a SR equilibrium, but not a LR equilibrium. 48 Q1 Q

49 SR V LR One firm in competitive industry Competitive market MC SRS1 AVC P E 1 1 D q1 q Q Because P E 1 > 1, Π > 0 for each firm. Industry is profitable, relative to other industries, so in the LR, there will be entry. 49

50 SR V LR One firm in competitive industry Competitive market MC SRS1 AVC P D q q Q Entry shifts SRS to the right, and P will fall. As P fall, Π shrink. But as long as Π > 0, incentive for further entry. 50

51 SR V LR One firm in competitive industry Competitive market MC AVC E1 SRS1 SRS2 P = E2 E2 MIN D qlr q Q Tells us that - in the LR - SRS shifts to SRS2. P = MIN, so Π = 0, for all firms. 51

52 SR V LR One firm in competitive industry Competitive market MC AVC E1 SRS1 SRS2 P = E2 E2 MIN D qlr q Q1 QLR Q E1 is a SR equilibrium but not a long run equilibrium E2 is both a SR and a LR equilibrium. Each firm in the industry produces qlr, so industry output = QLR. 52

53 LR COMPARATIVE STATICS Recall comparative statics exercises from Topic 3. - Curve shifts changed equilibrium. We need to learn how to do all these again, for both SR and LR. This is what you were doing (ahead of lecture) in lab this week. Key is to start in a LR equilibrium, then analyze some change. - For instance, a shift in the D curve. SR comparative statics will be more or less the same as in Topic 3. - Only change is the more complex cost story. New dimension re LR comparative statics. - If change makes Π > 0, there will be entry until Π = 0 again. - If change makes Π < 0, there will be exit until Π = 0 again. 53

54 COMPARATIVE STATICS One firm in competitive industry Competitive market P E 2 MC AVC D1 D2 E2 SRS1 E1 P E 1 q1 E1 is initial LR and SR equilibrium. q2 q Suppose D curve shifts from D1 to D2, so P in SR. New SR equilibrium is at E2. At P = P E 2, each firm q to q2, and earns > 0. > 0 means E2 cannot be LR equ, since there will be entry. 54 Q1 Q2 Q

55 COMPARATIVE STATICS One firm in competitive industry Competitive market P E 2 MC AVC D1 D2 E2 SRS1 SRS2 P E 1 E1 E3 q1 q2 q Q1 Q2 Q3 Q Entry increases SRS (rightward shift), which drives down P. Entry continues until P = P E 1=, so that = 0. E3 is new LR equilibrium: each firm goes back to producing q1and making = 0; overall more firms in the industry so Q = Q3. 55

56 ROUND-UP In Topic 7 we developed a model of production that is: - Richer than that seen in Topic 2. - Allows us to think about production in a modern market economy. All within the competitive market framework. We have learned distinction between short run & the long run. - In the short run, at least one factor is fixed. - In the long run, all factors are variable. In the short run, all relevant cost curves can be derived from information about the productivity of variable factors. - MPL gives us info about MC, APL gives us info about AVC. 56

57 ROUND-UP We learned that the analysis from Topics 3 and 4 was in fact short run analysis. - Implicitly (in most examples we looked at), we assumed that the number of firms was fixed. Now we understand the distinction between SR & LR equilibria. A short run equilibrium occurs when: 1. Each firm maximizes profits, taking P as given. - Chooses to produce q such that P (MR) = MC. 2. The given P is such that Q S = Q D, for fixed number of firms. 57

58 ROUND-UP A short run equilibrium occurs when: 1. Each firm maximizes profits, taking P as given. 2. The given P is such that Q S = Q D, for relevant number of firms. A long run equilibrium occurs when: 1. Each firm maximizes profits, taking P as given. 2. The given P is such that Q S = Q D, for relevant number of firms. 3. Capital flows ensure that P =. - Entry and exit ensure that econ profits equal zero. Note every LR equ. is a SR equ., but not every SR equ. is a LR equ. (Further note: You can disregard sections 13.4 and 14.3.e of the text on SR v LR cost curves.) 58

59 ROUND-UP Reminder: everything we did in Topic 7 was in context of perfectly competitive markets. - Assumptions of competitive market model: - All firms are price takers in all markets (outputs and inputs). - Each seller s output is identical (product homogeneity). - Capital can flow freely in the LR (can rephrase this as no barriers to entry ). In Topic 8 we will relax these assumptions, and analyze noncompetitive markets. 59