Transcript Chapter 8

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
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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:
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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
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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 profitmaximizing.
– 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 longrun 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?