ECON 311 MICROECONOMICS THEORY I

Transcription

1 ECON 311 MICROECONOMICS THEORY I Profit Maximisation & Perfect Competition (Short-Run) Dr. F. Kwame Agyire-Tettey Department of Economics Contact Information: fagyire-tettey@ug.edu.gh

2 Session Overview Given that it has desirable properties, perfect competition is useful for comparison with other market structure. This session presents an introduction to market structures and perfect competition. It also looks at the profit maximization conditions of a firm as well as the perfect competitive shortrun equilibrium. Slide 2

3 Session Outline Profit maximization condition of the firm Output choice Marginal revenue and price elasticity Introduction to Market Structure and Perfect Competition Market Structures Perfectly Competitive Market Competition in the Short-run Demand Curve Profit maximization Supply Curve Competitive Industry Equilibrium Slide 3

4 Learning Outcome After this session, you should be able to; Explain the concept of market structure. Outline the major assumptions of the perfectly competitive firm. Understand how competitive firms maximize profit in the short-run. Explain the short-run competitive demand and supply curve. Understand competitive equilibrium inthe Short Run. Slide 4

5 Reading List Read Chapter 8 of Jeffrey M. Perfloff (2012). Microeconomics (Sixth edition), Pearson Education Ltd. Read Chapter 23 and 24 of Hal R. Varian (2014). Intermediate Microeconomics, W. W. Norton and Company. Session slides Any other Economics textbook Slide 5

6 Modeling Firms Behaviour Economists see firms as single decision-making unit decisions are made by a single dictatorial manager who rationally pursues some goal - profit maximization A profit-maximizing firm chooses both its inputs and outputs with the sole goal of maximising profits seeks to maximize the difference between total revenue and total economic costs If firms are strictly profit maximizers, they will make decisions in a marginal way examine the marginal profit obtainable from producing one more unit of hiring one additional labourer 6

7 Output Choice Total revenue (TR) for a firm is given by R(q) = p(q)q In the production of q, certain economic costs are incurred [C(q)] Economic profits () are the difference between total revenue and total costs (TC) (q) = R(q) C(q) = p(q)q C(q) 7

8 Output Choice The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the function with respect to q equal to zero d dq ' ( q) dr dq dc dq 0 8 dr dq dc dq To maximize economic profits, the firm chooses an output which equates marginal revenue to marginal cost MR dr dq dc dq MC

9 Second-Order Conditions MR = MC is only a necessary condition for profit maximization For sufficiency, it is also required that 2 d 2 dq qq* d'( q) dq qq* 0 marginal profit must be decreasing at the optimal level of q 9

10 Profit Maximization revenues & costs Profits are maximized when the slope of the revenue function is equal to the slope of the cost function C R The second-order condition prevents us from mistaking q 0 as a maximum q 0 q* output 10

11 Marginal Revenue If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the good s price marginal revenue MR( q) dr dq d[ p( q) q] dq p q dp dq 11

12 Marginal Revenue and Elasticity The concept of marginal revenue is directly related to the elasticity of the demand curve facing the firm The price elasticity of demand is equal to the percentage change in quantity that results from a one percent change in price e q, p dq dp / / q p dq dp p q 12

13 Marginal Revenue and Elasticity This means that MR p q dp dq p1 q p dp dq p1 1 e q, p e q,p < -1 MR > 0 e q,p = -1 MR = 0 e q,p > -1 MR < 0 13

14 The Inverse Elasticity Rule Because MR = MC when the firm maximizes profit, we can see that MC p1 1 e q, p p MC p 1 e q, p The gap between price and marginal cost will fall as the demand curve facing the firm becomes more elastic 14

15 Introduction to Market Structures Slide 15

16 Let us pause for a moment Slide 16

17 Introduction (Market Structure) Market structure explains how firms in the market behave based on the market demand of consumers. It is defined by the characteristics that influence the behaviour and outcomes of the firms activities in that market. Several market structures exist. Examples include: Perfect competition imperfect competition monopoly oligopoly duopoly monopolistic competition Slide 17

18 Introduction (Market Structure) The structure of the market is determined by the following factors: Number of economic agents in the market (both sellers and buyers). Relative negotiation strength of the economic agents in terms of ability to set prices. Degree of concentration among the economic agents. Degree of product differentiation and homogeneity. Degree of barriers to entry and exit. Slide 18

19 Introduction (Perfectly Competitive Market) When there is a rivalry among the firms in the market for the same customers, they are termed as competitive firms. In that regard, a perfectly competitive market is a market in which there are large number of competitive firms such that it is difficult to single out a firm as an opponent. Perfect competition occurs where firms have no market power and hence do not react to each other. Examples of perfectly competitively markets include; market for many agricultural produce; stock exchange markets; retail and wholesale markets; among others. Slide 19

20 Introduction (Perfectly Competitive Market) Assumptions of Perfect Competition (Why demand curve is horizontal): 1. Firms sell homogenous or identical products; 2. Large number of sellers and buyers; 3. Free entry and exit; 4. Full information/perfect knowledge; 5. Negligible/low transaction costs; 6. Perfect mobility of productive resources. Note: The first two assumptions make competitive firms price-takers. If any competitive firm attempts to charge a higher price, its customers will buy the same product from elsewhere. Hence, there is no incentive to lower the price of a good since the firm can sell as many goods as possible at that market price. Slide 20

21 Introduction (Perfectly Competitive Market) The perfectly competitive firm faces a demand curve that is horizontal (perfectly/infinitely elastic) at the market price. The choice of the quantity of output to sell has no effect on price. Therefore, the firm can sell as many units of goods/output as it desires at the set market price, p. To maximize profit, a competitive firm ought to produce an output level that equates marginal cost (MC) to marginal revenue (MR); where MR equals market price (P). Also, MC should be rising or by producing nothing if average cost exceeds price at all outputs. MC(q) =MR(q)=P Therefore, a perfectly competitive firm is a quantity-adjuster, facing a perfectly elastic demand curve at the given market price and maximizing profit by choosing the output that equates its marginal cost to the market price. Slide 21

22 Competition in the Short-run Demand Curve of the Firm TR = P x Q AR = TR Q (Demand Curve) = P x Q Q Also, MR = TR Q = P P = AR = MR = P Price Figure 1 Demand Curve of the Industry/Market The horizontal summation of all individual demand curves. Thus, downward sloping, depicting a negative relationship between price and quantity. At higher prices, consumers will purchase a lesser quantity of the good At lower prices, all things being equal, consumers will purchase more of the product. Q D firm = AR = MR = P D market Quantity Slide 22

23 Competition in the Short-run (Profit Maximization) Economists usually assume that the goal of all firms (not only competitive firms) is profit maximization. A firm s profit (π) is defined by the difference between its total revenue (TR) and total cost (TC). The TC considered is the economics cost. This constitutes both explicit and implicit costs. Profit is represented mathematically as; π (q) = TR (q) TC (q) π q = TR q = TC q = 0 Hence, the first-order condition (FOC) for profit maximization is, MR (slope of TR curve)=mc (slope of TC curve). Since MR = P, the FOC might be written as MC = P. Slide 23

24 Competition in the Short-run (Profit Maximization) The second-order condition (SOC) for profit maximization requires that the second derivative of the profit function be negative. This is given as: 2 π q 2 = 2 TR q 2 2 TC q 2 < 0 Thus, 2 TR q 2 (slope of MR curve) < 2 TC q 2 (slope of MC curve). The SOC therefore requires that the slope of the MC curve to be steeper than that of the MR curve or the MC curve must cut the MR curve from below. In perfect competition, the slope of the MR curve is zero; resultantly, the SOC requires that the MC curve must have a positive/rising slope. This (SOC) is simplified as: 0 < 2 TC q 2 Slide 24

25 Competition in the Short-run (Profit Maximization) Optimum output level (TR/TC versus MR/MC): In Figure 2(a), the optimum quantity is where MR=MC. This same optimum quantity in Figure 2(b) provides the largest profit (gap between TR and TC) Figure 2(a): Total Cost and Total Revenue (GHS) Q Figure 2(b): Marginal Cost and Marginal Revenue (GHS) Q Slide TR TC MC MR

26 Total cost, revenue (GHC) Competition in the Short-run (Profit Maximization) Figure Loss Maximum profit= GHS 81 GHS 130 Loss TC Profit Quantity TR Slide 26

27 Profit Maximization Measuring a Firm s Profit To measure profit, simply subtract total cost from total revenue TR TC PQ ATC Q P ATC Q Graphically, profit is measured by computing the area of a rectangle Length = Q Height = the difference between P and ATC

28 Competition in the Short-run (Profit Maximization) Figure 4 Economic Profit (P > ATC): Here, the return on the existing allocation exceeds its opportunity cost. Price P Profit MC ATC D=MR=P AVC Total Cost Q Quantity Slide 28

29 Competition in the Short-run (Profit Maximization) Normal Profit (P = ATC): This is the breakeven profit where firms earn zero economic profit but normal profit. Normal profit is where the firm earns fair profit, such that the returns from exiting allocation is not different from its opportunity cost. Price P Figure 5 MC ATC D=MR=P AVC Total Cost = Total Revenue Q Quantity Slide 29

30 Competition in the Short-run (Profit Maximization) A firm encounters an economic Loss (P < ATC) when the return on the existing allocation is less than its opportunity cost. Price Figure 6 MC ATC In Figure 6, the firm should continue to operate because it covers part of its fixed cost or longterm unavoidable obligations. Thus, if the firm shuts down, it will incur a higher loss than if it continues to operate. P Loss Total Cost Q AVC D=MR=P Quantity A firm should only shut down if it cannot cover its variable costs. Slide 30

31 Determining Whether to Shut Down What happens if profit is negative? Should a firm shut down? In the short run, the firm still has to pay its fixed costs. If the firm shuts down, profits are given by shut down TR TC TR FC VC The difference is given by 0 FC 0 FC Alternatively, if the firm continues operating, operate TR TC TR FC VC operate shut down TR VC In general, firms should remain open and operating in the short run as long as revenue can cover variable costs, even if net profit is negative.

32 Determining Whether to Shut Down P > AVC: Continue operating Price & cost ( /unit) MC ATC Loss ATC* P* AVC* AVC d = MR Q* Quantity

33 Determining Whether to Shut Down Continue operating if TR VC or P AVC* where the * indicates the profit-maximizing (or loss-minimizing) quantity. Shut down if TR VC or P AVC* Continue operating as long as you cover your variable costs! If the price should fall below the minimum AVC then the firm s revenue cannot cover the cost incurred on the variable input and must shutdown Thus at the shutdown point: pq < TVC q or p = TVC q q = AVC

34 GHS per nut Competition in the Short-run (Supply Curve) MC S 5 E 3 p E 2 p 2 AVC 4 3 E 1 p E 0 p Quantity Figure 7. Marginal cost and average variable cost curves q 0 q 1 q 2 q 3 Quantity Figure 8. The supply curve Slide 34

35 Competition in the Short-run (Supply Curve) The competitive firm faces a supply curve which is same as the same shape of its MC curve above the level of AVC. The point E 0, where price, p 0, equals AVC is the shutdown point. As price rises from GHS 2 to GHS 5, the firm increases its production from q 0 to q 3 correspondingly. The firm s supply curve is shown in Figure 8. It relates market price to the quantity produced. The supply curve of a firm in perfect competition is its MC curve above the minimum AVC. The supply curve of a perfectly competitive industry is the sum of the MC curves its individual firms. Slide 35

36 Competition in the Short-run (Supply Curve) The market supply curve is derived on the assumption that factor prices and technology are given and that there is a large number of firms in the market. Thus the total market output at each price is the sum of the outputs supplied by all firms at the prevailing price. The shape of the market supply curve is dependent on: Technology; Factor prices and Size distribution of firms in the market. Note that the firms are not of the same sizes as there are different entrepreneurial efficiencies. These factors will determine the shape of the market supply because they determine the cost structure of the firms in the market and thus by extension determine the shape of the industry supply curve. Slide 36

37 Price Competition in the Short-run (Industry/Market Equilibrium) The short-run market price is determined by the intersection of the supply and demand curves. S p 0 E Market price D q 0 0 Quantity Slide 37

38 Producer Surplus for a Competitive Firm Marginal cost slopes upward; therefore, in most circumstances some output is being sold at a price above the cost of production. Producer surplus is the sum of the differences between marginal cost and the price of output at every level of output. This is equivalent to the difference between total revenue and total variable cost. PS TRVC

39 Producer Surplus for a Competitive Firm (a) Producer Surplus: Adding All of the Price-Marginal Cost Markups (b) Producer Surplus: Total Revenue Minus Variable Costs Price & cost ( /unit) MC Price & cost ( /unit) MC P d = MR P d = MR AVC* Producer surplus AVC AVC* Producer surplus AVC Both panels are equivalent. Q* Quantity Q* Quantity

40 Producer Surplus for a Competitive Firm Producer Surplus and Profit Producer surplus is closely related to profit, but they are not the same thing. PS TRVC, TRVC FC PS FC Firms will operate without making a profit, but they will shut down if they are not making any producer surplus.

41 Perfect Competition in the Short Run 8.3 Producer Surplus for a Competitive Industry Producer surplus for an entire industry is the sum of individual firms surplus.

42 Producer Surplus for a Competitive Firm Industry Producer Surplus: Producer surplus for an entire industry is the sum of individual firms surplus. Price Supply P Producer surplus Demand Q Quantity Remember that in the PC industry the supply curve is the marginal cost curve above minimum AVC.

43 Session Questions What defines a perfectly competitive market? Graphically distinguish between economic profit, normal profit, and economic loss. Explain the competitive firm s profit maximizing condition. With graphs and examples, illustrate how to derive the supply curve. Explain the short-run competitive equilibrium. Slide 43

44 Session Questions Assume that consumers view hair cuts as undifferentiated among producers, and that there are hundreds of barbers in a given market. The current market equilibrium price for a haircut is GH 15. Bob s Barbershop has a daily, short-run total cost given by: TC 0.5Q 2 with marginal cost MC Q Answer the following questions: a.how many haircuts should Bob prepare each day if his goal is to maximize profits? b.how much will he earn in profit each day?

45 Cardboard boxes are produced in a perfectly competitive market. Each identical firm has a short-run total cost curve of TC 3Q 3 18Q 2 30Q 50 where quantity is measured in thousands of boxes per week. The marginal cost of production is given by MC 9Q 2 36Q 30 Calculate the price below which a firm in the market will not produce any output (the shut-down price). Slide 45