Chapter 14: Firms in Competitive Markets

Transcription

1 Econ 3 Introduction to Economics: Micro Chapter 4: Firms in Competitive Markets Instructor: Hiroki Watanabe Spring 3 Watanabe Econ Profit Maximization / 67 Competitive Market Profit Maximization 3 Supply Curve 4 Aggregate Supply 5 Summary Watanabe Econ Profit Maximization / 67 Competitive Market Questions Market Environment Big Guys, Small Guys Profit Maximization 3 Supply Curve 4 Aggregate Supply 5 Summary Watanabe Econ Profit Maximization 3 / 67

2 Questions Question. (Agenda for Chpt 3-7) Where does the supply curve come from? What do firms do? 3 How does the market structure affect the firms decision making? Chpt 3: Preparation Chpt 4: Deriving the supply curve, perfect competition 3 Chpt 5: Monopoly 4 Chpt 7: Oligopoly 5 Chpt 6(?): Monopolistic competition Watanabe Econ Profit Maximization 4 / 67 Market Environment The objective (recall Assumption.3 in Chapter 3): Maximizing profit. Profit is total revenue minus total cost. total cost (Chpt 3) total revenue (below) Watanabe Econ Profit Maximization 5 / 67 Market Environment Competitive market satisfies the following (recall Definition.3 in Chapter 4): identical products infinitesimally small agents 3 free mobility 4 perfect knowledge 5 exclusion 6 rivalry 7 free entry Watanabe Econ Profit Maximization 6 / 67

3 Market Environment Total revenue differs from market to market. A firm in a competitive market has Total Revenue = price quantity = py. For a firm in a competitive market, p does not depend on their sales volume y. Proportional to the amount of output. This does not hold for monopolistic firms and oligopolistic firms. Watanabe Econ Profit Maximization 7 / 67 Market Environment Example. (Total Revenue for a Perfectly Competitive Firm) If the ongoing price is $6 in a perfectly competitive environment, then the total revenue when y slices are sold is TR(y) = 6y. Watanabe Econ Profit Maximization 8 / 67 Market Environment 36 TR(y) 3 Total Revenue [$] Watanabe Econ Profit Maximization 9 / 67

4 Market Environment Definition.3 (Marginal Revenue) is an additional revenue from an additional unit sold. It is the slope of the total revenue: MR(y) = ΔTR(y). Δy TR(y) increases by $6 by each slice in Example.. MR(y) won t be constant if p depends on y. Watanabe Econ Profit Maximization / 67 Market Environment 36 TR(y) MR(y) 3 TR, MR [$] Watanabe Econ Profit Maximization / 67 Big Guys, Small Guys Warning.4 (Big Guys, Small Guys) All the graphs in this chapter fall into either one of the following. Keep track. The big guy features unprocessed, raw economic variables. The small guy represents processed information obtained either by taking the average or differential of the corresponding big guy. Watanabe Econ Profit Maximization / 67

5 Big Guys, Small Guys big guy profit, producer surplus total revenue total cost variable cost fixed cost small guy marginal profit marginal revenue, price marginal cost, wage, average cost marginal cost, wage, average variable cost average fixed cost supply curve Watanabe Econ Profit Maximization 3 / 67 Big Guys, Small Guys Conversion for average Big guy divide by quantity small guy. Big guy multiply by quantity small guy. for marginal Big guy take a difference small guy. Big guy take an integral (area size) small guy. Watanabe Econ Profit Maximization 4 / 67 Big Guys, Small Guys Example.5 (Big and Small for Fixed Cost) Suppose Jack s fixed cost of production is $. Big guy: fixed cost FC =. Small guy: average fixed cost AFC(y) := FC y = y. Watanabe Econ Profit Maximization 5 / 67

6 Big Guys, Small Guys Fixed Cost (dollars) Cheesecake y (slices) Watanabe Econ Profit Maximization 6 / 67 Big Guys, Small Guys Average Fixed Cost (dollars) Cheesecake y (slices) Watanabe Econ Profit Maximization 7 / 67 Competitive Market Profit Maximization Profit Maximization Problem Finding the Optimal Scale 3 Supply Curve 4 Aggregate Supply 5 Summary Watanabe Econ Profit Maximization 8 / 67

7 Profit Maximization Problem Definition. (Profit Maximization Problem) A firm picks y that maximizes the profit: π(y) = TR(y) TC(y). Where is that y? How do we find it? Watanabe Econ Profit Maximization 9 / 67 Finding the Optimal Scale Instead of plugging in random y s in π(y), we ask: If Jack sells one more slice, does it increase his profit? If it does, go ahead. If it decreases the profit, downsize. 3 If it doesn t change, then that s the y he s looking for. Watanabe Econ Profit Maximization / 67 Finding the Optimal Scale Change in profit from an additional unit sold has two sources: MR(y): additional revenue that the additional unit brings in (just p in a perfectly competitive market) : additional cost that the additional unit inflicts (varies with y) Watanabe Econ Profit Maximization / 67

8 Finding the Optimal Scale Proposition. (Finding the Optimal Production Scale) The output level y that maximizes Jack s profit satisfies: MR(y) =. Watanabe Econ Profit Maximization / 67 Finding the Optimal Scale Example.3 (Finding the Optimal Production Scale) Suppose that Jack has the following production environment: y TR(y) TC(y) π(y) MR(y) Δπ Watanabe Econ Profit Maximization 3 / 67 Finding the Optimal Scale Total Revenue [$] TR(y) TC(y) π(y) Watanabe Econ Profit Maximization 4 / 67

9 Finding the Optimal Scale MR(y) 8 π(y) Total Revenue [$] Watanabe Econ Profit Maximization 5 / 67 Finding the Optimal Scale In general, y can be found where TC(y) is tangent to TR(y). p =.6 in the following. Watanabe Econ Profit Maximization 6 / 67 Finding the Optimal Scale 8 TC(y) TR(y) 6 π(y) Costs [$] Watanabe Econ Profit Maximization 7 / 67

10 Finding the Optimal Scale.5 Costs [$].5 MR(y) π(y)/ y Watanabe Econ Profit Maximization 8 / 67 Competitive Market Profit Maximization 3 Supply Curve Part of Supply Curve is Marginal Cost Curve Long-Run Supply Function 4 Aggregate Supply 5 Summary Watanabe Econ Profit Maximization 9 / 67 Part of Supply Curve is Marginal Cost Curve Recall from Definition 3. in Chapter 4: p s y=s(p) Watanabe Econ Profit Maximization 3 / 67

11 Part of Supply Curve is Marginal Cost Curve Supply function tells you for each price p, how much y would earn the largest profit. Try two different prices p =.6 and p =.8 and find corresponding s(p). Watanabe Econ Profit Maximization 3 / 67 Part of Supply Curve is Marginal Cost Curve 8 TC(y) TR(y) w/ p=.6 6 π(y) w/ p=.6 TR(y) w/ p=.8 π(y) w/ p= Watanabe Econ Profit Maximization 3 / 67 Part of Supply Curve is Marginal Cost Curve.5.5 MR(y) w/ p=.6 π(y)/ y w/ p=.8 MR(y) w/ p=.6 π(y)/ y w/ p= Watanabe Econ Profit Maximization 33 / 67

12 Part of Supply Curve is Marginal Cost Curve What it boils down to is, supply is determined via the marginal cost. Note that the MC itself was derived by asking For each y, what s the additional cost we have to incur by switching to y +? Here, the question is For each p, what s the amount y that maximizes the profit? Watanabe Econ Profit Maximization 34 / 67 Part of Supply Curve is Marginal Cost Curve Watanabe Econ Profit Maximization 35 / 67 Part of Supply Curve is Marginal Cost Curve Recap: y is where MR(y) =. In a perfectly competitive market, MR(y) = p. 3 Then y = s(p) can be found where = p. Watanabe Econ Profit Maximization 36 / 67

13 One problem: Proposition. does not guarantee π >. All it does is to maximize π(y), be it positive or negative. And π(y) can be negative if the price is too low. If that happens, what is the point of staying in business? Watanabe Econ Profit Maximization 37 / 67 Short-run supply (fixed K ) Long-run supply ( K can be altered as well) Watanabe Econ Profit Maximization 38 / 67 In the short run, rent payment on K is a done deal. Jack has to pay the rent till his contract is up. It does not affect his short-run decision making because it is Definition 3. (Sunk Cost) is the amount Jack has already paid or promised to pay. It cannot be recouped. Watanabe Econ Profit Maximization 39 / 67

14 Definition 3. (Short-Run Profit Maximization Problem) In the short run, Jack maximizes π S (y) = py VC(y). () Watanabe Econ Profit Maximization 4 / 67 Jack has to maximize the profit ( Proposition. ). make sure that the π S (y) is positive. Watanabe Econ Profit Maximization 4 / 67 Rewrite () as: π S (y) = py VC(y) πs (y) y = p AVC(y). If the price drops lower than the smallest AVC(y), then Jack incurs loss. AVC(y) s lowest point is marked by y SD (Chpt 3). Watanabe Econ Profit Maximization 4 / 67

15 For each p, the quantity supplied is determined by p =, however if p becomes lower than AVC(y SD ), s(p) =. Watanabe Econ Profit Maximization 43 / 67.5 TR() VC() AVC(y) Watanabe Econ Profit Maximization 44 / 67.5 VC(6) TR(6) AVC(y) Watanabe Econ Profit Maximization 45 / 67

16 .5 VC(5/) TR(5/) AVC(y) Watanabe Econ Profit Maximization 46 / 67 Proposition 3.3 () In the short run, supply is for p < AVC(y SD ). coincides with for p AVC(y SD ). (y SD, AVC(y SD )) is called a shutdown point. Watanabe Econ Profit Maximization 47 / 67 AVC(y) Short Run Supply Watanabe Econ Profit Maximization 48 / 67

17 Long-Run Supply Function In the long run, the fixed cost is not a sunk cost. Jack can avoid the fixed cost as he sees fit. The problem with Proposition. still remains: Proposition. maximizes π(y), but it can be negative. Jack had better close his business if the price is so low that π(y). Watanabe Econ Profit Maximization 49 / 67 Long-Run Supply Function Jack stays in business in the long run if π(y) := py TC(y) p ATC(y). The lowest price that Jack engages in production is ATC(y MES ) (c.f., Chapt 3) Watanabe Econ Profit Maximization 5 / 67 Long-Run Supply Function.5 TR() TC() ATC(y) Watanabe Econ Profit Maximization 5 / 67

18 Long-Run Supply Function.5 TC(6) TR(6) ATC(y) Watanabe Econ Profit Maximization 5 / 67 Long-Run Supply Function.5 TC(7.9895) TR(7.9895) ATC(y) Watanabe Econ Profit Maximization 53 / 67 Long-Run Supply Function Proposition 3.4 (Long-Run Supply Function) In the long run, supply is for p < ATC(y MES ). coincides with for p ATC(y MES ). (y MES, ATC(y MES )) is called a break-even point. Watanabe Econ Profit Maximization 54 / 67

19 Long-Run Supply Function ATC(y) Long Run Supply Watanabe Econ Profit Maximization 55 / 67 Long-Run Supply Function ATC(y) AVC(y) Watanabe Econ Profit Maximization 56 / 67 Long-Run Supply Function p y on p = py TC(y) Long Run py VC(y) Short Run - Out - Out - Out - Out AVC(y SD ) y SD - Out In/Out - Out + In ATC(y MES ) y MES In/Out + In + In + In Watanabe Econ Profit Maximization 57 / 67

20 Competitive Market Profit Maximization 3 Supply Curve 4 Aggregate Supply Short-Run Aggregate Supply Long-Run Aggregate Supply 5 Summary Watanabe Econ Profit Maximization 58 / 67 Short-Run Aggregate Supply In the short run, the number of firms are fixed. In the long run, it is endogenous. Watanabe Econ Profit Maximization 59 / 67 Short-Run Aggregate Supply Short-run aggregate function is just a (horizontal) sum of individual supply (C.f., Chpt 4). Watanabe Econ Profit Maximization 6 / 67

21 Short-Run Aggregate Supply AVC(y) Short Run Supply Watanabe Econ Profit Maximization 6 / 67 Long-Run Aggregate Supply In the long run, If p > ATC(y MES ), π(y) >. New firms enter the market. Drops the price. If p < ATC(y MES ), π(y) <. Existing firms leave the market. Increases the price. 3 If p = ATC(y MES ), π(y) =. Nobody leaves nor enter the market (long-run equilibrium). Price stays the same. Watanabe Econ Profit Maximization 6 / 67 Long-Run Aggregate Supply Long-run supply curve is perfectly elastic. Horizontal at p = ATC(y MES ). Watanabe Econ Profit Maximization 63 / 67

22 Competitive Market Profit Maximization Supply Curve Aggregate Supply Competitive Market Profit Maximization 3 Supply Curve 4 Aggregate Supply 5 Summary Watanabe Econ 4935 Competitive Market 4 Profit Maximization Profit Maximization Supply Curve 64 / 67 Aggregate Supply Firms decision making and supply function Two conditions to find the supply curve Watanabe Econ 4935 Competitive Market 4 Profit Maximization Profit Maximization Supply Curve 65 / 67 Aggregate Supply Airline du Jour Today s color theme is provided by courtesy of Watanabe Econ 4935 Garuda Indonesia 4 Profit Maximization 66 / 67

23 average cost, 3 average fixed cost, 3 average variable cost, 3 break-even point, 54 fixed cost, 3 long-run equilibrium, 6 long-run supply function, 54 marginal cost, marginal profit, 3 marginal revenue,, 3, profit, 3 profit maximization problem, 9 short-run profit maximization problem, 4 short-run supply function, 47 shutdown point, 47 sunk cost, 39, 49 supply function, 3 total cost, 3 total revenue, 8, 3 variable cost, 3 wage, 3 Watanabe Econ Profit Maximization 67 / 67