Lecture Notes
Firm Supply in Competitive Markets
 Market Environment: ways firms interact in making
pricing and output decisions.
 Possibilities: (1) Perfect Competition
(2) Monopoly
(3) Oligopoly
(4) Imperfect Competition (monopolistic)
 In P.C. p=fixed for the producer
 Why? => small firms, identical products, large number of firms
 Examples
 Firms are price takers at market prices
P
S
D market
O
OR
P
P*
P*
Don’t usually worry
about p < p* since
these firms are
typically smaller and
can’t produce much
df
D market
y
y
 The firm’s problem is to max
= py - c(y)
 Is this a long run or a short run problem?
 ∆R = p ∆ y + ∆ p y => ∆R/ ∆y = p = MR
 But p = MR


Why?
∆C/ ∆ y = MC
 Choose to produce where MR=MC
 Why does this make sense?
 Exceptions to the Rule
P
mc
A
P*
 A= point of
 Why?


B
Df
Y
minimization
MC downward sloping => increasing y, decreasing mc =>
Decreasing C
MR=>
increases as y increases
 B= point of
maximization
 (1) any movement from A increases
 (2) any movement from B decreases
 Idea of second order conditions
 What does that mean?
 First order conditions : MR=MC
 Second order condtions: slope of MC > 0


Or slope of MC > Slope of MR = o
=> B is the correct point
 2nd Exception—Shut Down
 Short-Run: if shut down => lose fixed costs (F)
 When is this better than operating?


= -F if y =0
= py – Cv (y) – F if y>0
 So if –F > py – Cv(y) – F => shutdown or
 Cv(y) > py
 Or Cv(y)/(y) > p or p < AVC => shutdown
 Similarly in the Long Run:

= py – C(y) or p < AC
= 0 if shutdown
 A= Short Run shut down point
 B = Long Run shut down point
p
AC
AVC
B
A
Y
$
MC
LRAC
A
y
A = LR shut-down point
Short Run Supply = portion of MC
Above point A in 1st graph
Also LR Supply = portion of LRMC above LRAC
loss minimization
Profit (graphically)
MC
AC
p
AVC
P*
Df
Also Inverse Supply
2 Choices:
y*
y
(1) Ps = S (y)
(2) y= S (P)
 Profit = the shaded area in the graph





=p*y* - AC(y*) y*
TR
TC
Since AC(y*) = TC(y*)/y*
Now more carefully define producer surplus.
Recall:
p
Producer surplus
S
P*
y*
Y
p
MC
MC
p
AC
AC
P*
AVC
y*
P*
Y
Producer Surplus = the shaded area in the graph
Why are the two graphs equivalent?
AVC
y*
Y
 Why is Producer’s Surplus relevant if profit matters?
 In SR must be true that ∆PS=∆
 Why? Fixed costs don’t change as y changes in SR
 L-R Supply Curve
 S-R Supply Curve = MC above AVC

Where MR=MC
P= MC (y, k) – k is fixed
 L-R Supply Curve = same with K variable

=> where MR = MC
 P = MC (y, k(y))
 K is optimal
 In L-R
> 0 or Py – C(y) > 0
 Or p > c(y)/y or P > ATC
Lmc
$
LR Supply
Constant Returns to Scale
L atc
$
Cmin
L atc = Lmc
y
What is LR Supply?
y
 Relationship between long-run and short-run supply
curve for a given firm is given by:
p
SSR
SLR
Y1
Y
 Why would SLR be more elastic (more responsive to
price changes)?
 Can change both K & L optimally in the L-R =>
 Increase y at lower cost beyond y1 in the LR
 Note: (Producer Surplus)LR =
variable.
LR
since all inputs are
 In the short-run, firms can be found with 3 different
situations where y > 0.
MC
AC
AVC
p
P*
Df
y*
1) π > 0, y > 0
y
MC
AC
AVC
p
Df
P*
y*
2) π = 0, y > 0
y
p
MC
AC
AVC
P*
Df
y*
y
3) π < 0, y > 0; why is y>0?
 What is the short-run industry supply?
 S = Σ Si (P) = Σ MCi for all i firms.
 Recall that firm short-run supply = firm’s MC curve
above AVC.
 Long-Run Equilibrium in Perfect Competition
 No fixed inputs.
 Free entry and exit.
 Consider firms of type 3 above ( π < 0 but p > AVC) who
still produce in short-run. What happens?

No fixed costs => observe exit in the market and π rises to
zero.
 Consider firms of type 1 above (π > 0). What happens?

The positive π serves as a signal to other firms to enter => π
falls to zero.
 The long equilibrium occurs where π equals 0.

What does this look like, assuming all firms have the same
costs?
MC
LRAC=AVC
p
P*
Df
y*
y
 Notice that y* must occur where LRAC is at its
minimum. Why?
 Also p* = C(y*) => π = 0.
 What does LR industry supply curve look like if firms
are large relative to the market?
 Assume that all firms are the same => industry supply in
SR = Σ MCi = nMC; where i=n (i.e., n = the the total
number of firms.
 Suppose that there are 4 possible firms then get:
p
S1
S2
S3
S4
P*
D1
Y
p
S1
S2
S3
S4
P1
P*
D2
D1
Y1
Y2
Y
 Notice that equilibrium p and y is given by the lowest
possible price where p1 ≥ p* and y* is at that
intersection.
 Thus, if D = D1 then p = p1 and Y = Y1
 If D = D2 the p = p1 and Y = Y2
 With large plants then long-run supply looks like:
p
S1
S2
S3
S4
P*
Y
 P* = the minimum LRAC.
 The above is with only 4 firms total.
 What if firms are all very small with respect to the
market?
p
P*
SLR = min LRAC
Y
 Taxes
 The graph below shows the SLR both before and after a
tax is imposed.
p
SLR after tax
P*+ tax
P*
tax
SLR before tax
Y
 Where is the equilibrium?
 For that must have Demand and SSR
p
SSR
SSR
P*+ tax
P1
P*
SLR after tax
tax
SLR before tax
D
Y
 Short-run Equilibrium is at P1 therefore, both firms and
consumers pay tax.
 Long-run Equilibrium is at P* + tax therefore only
consumers pay tax in long-run.
 Before assumed that costs were constant with entry.
 Is that a reasonable assumption?
p
P*
p
SLR = min
LRAC
Y
Increasing costs with entry
P*
SLR = min
LRAC
Y
Decreasing costs with entry
 Economic Rent
 Suppose that we look at the rent earned by a highly paid
sports or entertainment individual.
 Do D and S still determine price?

Yes.
p
S
P*
D
Y
 D and S still determine price but what economic rent
is the player getting?
 That is, due to a talent restriction, there is no free entry





for the players.
Can profit be driven to zero under these conditions?
Suppose fixed supply of Peyton Manning and his
opportunity cost = $100,000 but his MP in football = $10
m.
Profits are driven to zero just for the firm producing the
product (i.e., NFL team).
The economic rent is the payment for the fixed factor(s)
= total fixed costs.
What is rent seeking behavior?
 What affects the size of the rent?
 Depends upon the fixed supply for the talent market
(Peyton Manning) and the no-talent market (me).
p
S
p
S
P*
D
D
Y
Talent Market
Y
NoTalent Market
 Final notes on Perfect Competion
 Assume that we generally having an increasing cost
industry with an upward sloping long-run industry
supply.
 This leads to an equilibrium that is allocatively efficient.

One that maximizes net surplus (i.e., MSB = MSC or no
deadweight losses).
p
S=MSC
P*
D=MSB
Y*
Y