THE FIRM AND THE MARKET

Transcription

1 Prerequisites Almost essential Firm: Demand and Suly THE FIRM AND THE MARKET MICROECONOMICS Princiles and Analysis Frank Cowell Note: the detail in slides marked * can only be seen if you run the slideshow July

2 Introduction In revious resentations we ve seen how an otimising agent reacts to the market Use the comarative statics method We could now extend this to other similar roblems But first a useful exercise in microeconomics: Relax the secial assumtions We will do this in two stages: Move from one rice-taking firm to many Dro the assumtion of rice-taking behaviour July

3 Overview The Firm and the Market Issues in aggregating suly curves of ricetaking firms Market suly curve Size of the industry Basic aggregation Large numbers Interaction amongst firms Price-setting Product variety July

4 Aggregation over firms We begin with a very simle model Two firms with similar cost structures But using a very secial assumtion First we look at the method of getting the market suly curve Then note the shortcomings of our articular examle July

5 A market with two firms Suly curve firm 1 (from MC) Suly curve firm 2 Pick any rice Sum of individual firms suly Reeat The market suly curve q 1 q 2 q 1 +q 2 low-cost firm high-cost firm both firms July

6 Simle aggregation Individual firm suly curves derived from MC curves Horizontal summation of suly curves Market suly curve is flatter than suly curve for each firm But the story is a little strange: See resentation on duooly Each firm act as a rice taker even though there is just one other firm in the market Number of firms is fixed (in this case at 2) Firms' suly curve is different from that in revious resentations relaxed later in this resentation July

7 Another simle case Two rice-taking firms Similar iecewise linear MC curves: Each firm has a fixed cost Marginal cost rises at the same constant rate Firm 1 is the low-cost firm Analyse the suly of these firms over three rice ranges July

8 Market suly curve (2) Below ' neither firm is in the market Between ' and '' only firm 1 is in the market Above '' both firms are in the market ' " " ' q 1 q 2 q 1 +q 2 low-cost firm high-cost firm both firms Now for a roblem July

9 Where is the market equilibrium? Try (demand exceeds suly ) demand Try (suly exceeds demand) " suly There is no equilibrium at " q July

10 Lesson 1 Nonconcave roduction function can lead to discontinuity in suly function Discontinuity in suly functions may mean that there is no equilibrium July

11 Overview The Firm and the Market A simlified continuity argument Market suly curve Size of the industry Basic aggregation Large numbers Interaction amongst firms Price-setting Product variety July

12 A further exeriment The roblem of nonexistent equilibrium arose from discontinuity in suly But is discontinuity likely to be a serious roblem? Work through another examle Similar cost function to revious case This time identical firms (Not essential but easier to follow) July

13 Take two identical firms ' ' q 1 q July

14 Sum to get aggregate suly ' q 1 + q 2 July

15 * Numbers and average suly Rescale to get average suly of the firms Comare with S for just one firm Reeat to get average S of 4 firms average S of 8 firms of 16 firms Two more dots! ' There s an extra dot! average(q f ) July

16 The limiting case The limit: continuous averaged suly curve A solution to the non-existence roblem? A well-defined equilibrium Firms oututs in equilibrium average demand average suly ' average(q f ) (3/16)N of the firms at q=0 (13/16)N of the firms at q=16 July

17 Lesson 2 A further insight into nonconcavity of roduction function (nonconvexity of roduction ossibilities) Yes, nonconvexities can lead to roblems: Discontinuity of resonse function Nonexistence of equilibrium But if there are large numbers of firms then then we may have a solution The average behaviour may aear to be conventional July

18 Overview The Firm and the Market Introducing externalities Market suly curve Size of the industry Basic aggregation Large numbers Interaction amongst firms Price-setting Product variety July

19 Interaction amongst firms Consider two main tyes of interaction Negative externalities Pollution Congestion Positive externalities Training Networking Infrastructure Other interactions? For examle, effects of one firm on inut rices of other firms Normal multimarket equilibrium Not relevant here July

20 Industry suly: negative externality Each firm s S-curve (MC) shifted by the other s outut The result of simle ΣMC at each outut level Industry suly allowing for interaction S 1 (q 2 =5) S 2 (q 1 =5) S MC 1 +MC 2 S 1 (q 2 =1) S 2 (q 1 =1) MC 1 +MC 2 q 1 q 2 q 1 + q 2 firm 1 alone firm 2 alone both firms July

21 Industry suly: ositive externality Each firm s S-curve (MC) shifted by the other s outut The result of simle ΣMC at each outut level Industry suly allowing for interaction S 1 (q 2 =1) S 2 (q 1 =1) MC 1 +MC 2 MC 1 +MC 2 S S 1 (q 2 =5) S 2 (q 1 =5) q 1 q 2 q 1 + q 2 firm 1 alone firm 2 alone both firms July

22 Positive externality: extreme case MC 1 +MC 2 S MC 1 +MC 2 q 1 + q 2 both firms July

23 Externality and suly: summary Externalities affect roerties of resonse function Negative externality: Suly less resonsive than the sum-of-the-mc rule indicates Positive externality: Suly more resonsive than the sum-of-the-mc rule indicates Could have forward-falling suly curve July

24 Overview The Firm and the Market Determining the equilibrium number of firms Market suly curve Size of the industry Price-setting Product variety July

25 The issue Previous argument has taken given number of firms This is unsatisfactory: how is the number to be fixed? should be determined within the model Determination within model: by economic behaviour of firms by conditions in the market Look at the entry mechanism base this on revious model must be consistent with equilibrium behaviour Begin with equilibrium conditions for a single firm July

26 Analysing firms equilibrium rice = marginal cost determines outut of any one firm rice average cost determines number of firms An entry mechanism: If the C/q ga is large enough then this may ermit another firm to enter Alying this rule iteratively enables us to determine the size of the industry July

27 Outline of the rocess (0) Assume that firm 1 makes a ositive rofit (1) Is q C set-u costs of a new firm? if YES then sto. We ve got the eqm # of firms otherwise continue: (2) Number of firms goes u by 1 (3) Industry outut goes u (4) Price falls (D-curve) and individual firms adjust outut (individual firm s S-curve) (5) Back to ste 1 July

28 * Firm equilibrium with entry Draw AC and MC Get suly curve from MC rice marginal cost average cost Use rice to find outut Profits in temorary equilibrium Allow new firms to enter Π 1 q N q 4 q 3 q 21 outut of firm In the limit entry ensures Price-taking rofits are cometed temorary away equilibrium = C/q n f = 1234 n f = N July

29 Overview The Firm and the Market The economic analysis of monooly Market suly curve Size of the industry Price-setting Product variety July

30 The issues We've taken for granted a firm's environment What basis for the given rice assumtion? What if we relax it for a single firm? Get the classic model of monooly: An elementary story of market ower A bit strange what ensures there is only one firm? The basis for many other models of the firm July

31 A simle rice-setting firm Comare with the rice-taking firm Outut rice is no longer exogenous We assume a determinate demand curve No other firm s actions are relevant Profit maximisation is still the objective July

32 Monooly model structure We are given the inverse demand function: = (q) Gives the rice that rules if the monoolist delivers q to the market For obvious reasons, consider it as the average revenue curve (AR) Total revenue is: (q)q Differentiate to get monoolist s marginal revenue (MR): (q)+ q (q)q q ( ) means d( )/dq Clearly, if q (q) is negative (demand curve is downward sloing), then MR < AR July

33 Average and marginal revenue AR curve is just the market demand curve Total revenue: area in the rectangle underneath Differentiate total revenue to get marginal revenue (q)q d(q)q dq (q) MR AR q July

34 Monooly otimisation roblem Introduce the firm s cost function C(q) Same basic roerties as for the cometitive firm From C we derive marginal and average cost: MC: C q (q) AC: C(q) / q Given C(q) and total revenue (q)q rofits are: Π(q) = (q)q C(q) The shae of Π is imortant: We assume it to be differentiable Whether it is concave deends on both C( ) and ( ) Of course Π(0) = 0 Firm maximises Π(q) subject to q 0 July

35 Monooly solving the roblem Problem is max Π(q) s.t. q 0, where: Π(q) = (q)q C(q) First- and second-order conditions for interior maximum: Π q (q) = 0 Π qq (q) < 0 Evaluating the FOC: (q) + q (q)q C q (q) = 0 Rearrange this: (q) + q (q)q = C q (q) Marginal Revenue = Marginal Cost This condition gives the solution from above get otimal outut q * ut q * in ( ) to get monoolist s rice: * = (q * ) Check this diagrammatically July

36 Monoolist s otimum AR and MR Marginal and average cost Otimum where MC=MR Monoolist s otimum rice MC Monoolist s rofit AC * Π q* MR AR q July

37 Monooly ricing rule Introduce the elasticity of demand η: η := d(log q) / d(log ) = (q) / q q (q) η < 0 First-order condition for an interior maximum (q) + q (q)q = C q (q) can be rewritten as (q) [1+1/η] = C q (q) This gives the monoolist s ricing rule: (q) = C q(q) 1 + 1/η July

38 Monooly the role of demand Suose demand were changed to a + b(q) a and b are constants Marginal revenue and demand elasticity are now: MR(q) = b q (q) q + [a + b(q) ] η = [a/b+ (q) ] / q q (q) Rotate the demand curve around ( *,q * ) db > 0 and da = (q * ) db < 0 Price at q * remains the same Marginal revenue at q * decreases: dmr(q * ) < 0 Abs value of elasticity at q * decreases: d η < 0 But what haens to otimal outut? Differentiate FOC in the neighbourhood of q * : dmr(q * )db + Π qq dq * = 0 Since dmr(q * ) < 0, Π qq < 0 and db > 0 we have dq * < 0 July

39 Monooly analysing the otimum Take the basic ricing rule (q) = C q (q) 1 + 1/η Use the definition of demand elasticity (q) C q (q) (q) > C q (q) if η < rice > marginal cost Clearly as η decreases: outut decreases ga between rice and marginal cost increases What haens if η 1 (η -1)? July

40 Monooly no solution? To understand why there may be no solution consider two examles A firm in a cometitive market: η = (q) = A monooly with inelastic demand: η = ½ (q) = aq 2 Same quadratic cost structure for both: C(q) = c 0 + c 1 q + c 2 q 2 Examine the behaviour of Π(q) July

41 Profit in the two examles Π discontinuity q* q η = η = ½ July

42 The result of simle market ower There's no suly curve: For cometitive firm market rice is sufficient to determine outut Here outut deends on shae of market demand curve Price is artificially high: Price is above marginal cost Price/MC ga is larger if demand is inelastic There may be no solution: What if demand is very inelastic? July

43 Overview The Firm and the Market Modelling monoolistic cometition Market suly curve Size of the industry Price-setting Product variety July

44 Market ower and roduct diversity Each firm has a downward-sloing demand curve: like the case of monooly Firms roducts may differ one from another new firms can enter with new roducts diversity may deend on size of market Introduces the concet of monoolistic cometition Follow the method cometitive firm: Start with the analysis of a single firm Entry of new firms cometes away rofits July

45 Monoolistic cometition: 1 MC AC Take linear demand curve (AR) The derived MR curve Marginal and average costs Otimal outut for single firm Price and rofits Π 1 q 1 MR AR outut of firm outcome is effectively the same as for monooly July

46 Monoolistic cometition: 2 Zero Profits q 1 outut of firm July

47 Review Individual suly curves are discontinuous: a roblem for market equilibrium? A large-numbers argument may hel The size of the industry can be determined by a simle entry model With monooly equilibrium conditions deend on demand elasticity Monooly + entry model yield monoolistic cometition July

48 What next? We could move on to more comlex issues of industrial organisation Or aly the insights from the firm to the consumer July