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.

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.

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.

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.

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.

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*.

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).

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.

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).

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?

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).

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*.

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 .).

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 )

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.

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.

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.

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.

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).

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.

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?