Ch 8: Profit Max Under Perfect Competition

1. Ch 8: Profit Max Under Perfect Competition • Three assumptions in p.c. model: • 1) Price-taking: many small firms, none can affect mkt P by ing Q  no mkt power. Firm can sell all it wants at mkt P so faces perfectly elastic (horizontal) product demand curve. • 2) Product homogeneity: each firm produces nearly identical product all are perfect substitutes. This assures there will be single mkt P • 3) Free entry and exit: assures big number of firms in industry.

2. More on Perfect Competition • Real-life examples mostly found in agriculture. • Large # firms means 10 – 20 firms in industry. • P.C. model is an ideal; serves as useful starting point. • Additional assumption: • Firms’ goal is to maximize profits (good assumption given large # firms). • Principal-agent problems more in news lately; to be discussed later. • -max goal extends beyond P.C. market structure.

3. Profit Maximization • Define profit = TR – TC • (q) = R(q) – C(q), or •  = R – C. • q* represents firm’s -max level of output. • To achieve  -max: firm picks q* where difference between TR and TC is greatest. • With graphs of TR and TC: max  where have greatest vertical distance between TR and TC.

4. Three Curves in Figure 8.1 • TR: slope is MR • TC: slope is MC. •  function: see inverse U-shape: plots out vertical distance between TR and TC. • Max  where: • 1) TR – TC is largest • 2) slope TR = slope TC; or • MR = MC. • 3) Rule for all firms (PC or not): • pick -max q* where MR = MC.

5. Review Implications of Perfect Competition • Keep terms straight: • Q = market output; • D = market demand; • q = firm output; • d = firm demand. • Market D is downward sloping but demand curve faced by individual firm is perfectly elastic (horizontal). • Interpret: firm can sell all it wants to sell at the single market price. • In other words, its selection of q* has no impact on market price. • So: firm demand curve is same as its MR curve.

6. Further Implications of P. C. Model • Recall under PC: firm’s demand curve is its MR curve. • This means that P  MR. • Profit-max rule for PC firm:Pick -max q* where MC = MR = P. • Also, since P  MR for each q, then P = MR = AR. • Draw simple graph to see -max q*.

7. FURTHER Details • Revise rule: pick -max q* where MR = MC AND MC is rising. • Recall: this rule applies to all firms, not just p.c. firms. • Short Run profit for p.c. firm: • P - ATC at q* = average profit per unit of q. • Recall:  = TR – TC; So: • /q = TR/q – TC/q • Avg.  = P – ATC. • Total  at q* = q*  (P-ATC).

8. Firm’s SR Shutdown Decision • Situation: What if, in the SR, -max q* results in losses? • Firm must choose (1) vs (2): • 1) Continue producing at q* and incurring the full losses. • 2) Shutdown in SR (I.e., produce q-0) , which will reduce losses but firm still must pay FC and now have NO revenues.

9. SR Shutdown Rule • At q*, firm must know:: • P, • ATC, and • AVC. • Rule: • If   0 in SR (so P  ATC at q*): continuing producing q* as long as P  AVC. • In other words: continue to produce q* as long as firm is covering operating costs. • In LR: any negative profits will cause shutdown and exit from industry. (So: LR shutdown if P  ATC).

10. Exercise • Coffee mug company: P = $8. • Currently, q = 200; • MC = $10 = ATC. • If did have q=150, then: • MC = $6 = AVC. • Questions: With -max goal: • 1. Should firm stick with q=200, reduce, or increase? • 2. Would shut-down be better?

11. Competitive Firm’s SR Supply Curve • Supply Curve: shows q produced at each possible price. • SR supply curve: the firm’s MC curve for all points where MC  AVC. • I.e., -max q* is where P  AVC. • Remember “trigger” for shutdown in SR implies that MC curve has an irrelevant part (where MC  AVC).

12. Firm’s Response to  Price of Input • Consider:  price input  causes  MC at each q  shift up to left of MC curve. • See Figure 8.7: • Start at P = $5 with MC1; so q* = q1. • Now: price input causes  MC: • Shifts MC up to left. • Causes  q*.

13. SR Market Supply Curve • Shows: amount of Q the industry will produce in SR at each possible price. • Sum SR supply curves for firms using horizontal summation. • That is: at each possible price, sum up total quantity supplied by each firm. • See Figure 8.9. • (Note that we are assuming that, for each firm, as q es, individual MC curves no .).

14. Price Elasticity of Market Supply • ES = %Qs/1%P • = (Q/Q) / (P/P). • ES  0 always because SMC slopes upward. • If MC  a lot when Q (or, costly to Q), then ES is low. • Extreme cases: • Perfectly inelastic S: vertical. • When industry’s plant and equipment so fully utilized that greater output can be achieved only if new plants built. • Perfect elastic S: horizontal (MC no  when Q )

15. Producer Surplus in SR • Concept analogous to CS. • For rising MC: P  MC for every unit of q except last one produced. • For a firm (see Figure 8.11): • For all units produced (up to q*):sum the differences between mkt P and MC of production. • Measures area above MC schedule (S curve) and below mkt price.

16. LR Competitive Equilibrium • If each firm earns zero economic , each firm is in LR equilibrium. • Three conditions: • 1. All firms in industry are profit-maximizing. • 2. No firm has incentive to enter or leave industry (due to  = 0). • 3. P is that which equates QS = QD in market.

17. Adjustment from SR to LR Equilibrium • Firm starts in SR equilibrium. • Positive profits induce new firms to entire industry so industry S curve shifts rightward. • This causes market P to fall. • This causes firm’s MR line to fall, until profits = 0 again. • Key: firms enter as long as P  ATC • Note: in this case, MC no shift due to constant cost assumption. • LR choice of q*: • where LMC = P = MR = LAC. • Key is LMC=LAC.

18. Economic Rent • Economic Rent: • Difference between what a firm is willing to pay for an input and the minimum amount necessary to buy the input. • For an industry: economic rent is same as LR producer surplus. • For a fairly fixed factor (like land): bulk of payments for the factor is rent (so factor S curve is vertical). • In LR in a competitive mkt: PS that firms earn for Q is the economic rent from all its scarce inputs. • Presence of economic rent can explain why profits might persist in LR.

19. Industry’s LR Supply Curve • Cannot just sum individual firms horizontally because as price es, # firms in industry es. Must connect the zero-profit points. • Shape of LR supply curve: depends on whether (and in what direction) the es in each firm’s q causes es in input prices. • Constant cost industry: As q and Q , input prices no  so firm’s MC, AVC, and ATC NO shift as q changes. • Here, long run industry supply curve is flat (perfectly horizontal). • Example: coffee industry (land for growing coffee widely available).

20. Other Cost Structures • Increasing cost industry • Example: oil industry (limited availability of easily accessible, large-volume oil fields, so to  q, firms costs rise too). • Result is upward-sloping long run industry supply curve. • Decreasing cost industry • Example: automobile industry (AC falls as industry output rises) • Result is downward-sloping long run industry supply curve.

21. Exercise • In an increasing cost industry starting in LR equilibrium: • What is the immediate and then long-run effect of a shift to the left in market demand? Show and discuss the process of return to LR equilibrium. • 1. Will the market price rise, fall, or stay the same? • 2. What are the effects on the long-run market quantity and the long-run firm quantity? • 3. What is the shape of the long-run supply curve? • 4. What would be different if the industry were a constant cost industry? Decreasing cost industry?