Post on 13-Jan-2016
Lecture Notes
Firm Supply in Competitive MarketsMarket 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 pricesS
D market
P
O
P*
P
y
OR
Don’t usually worry about p < p* since these firms are typically smaller and can’t produce much
P*df
y
D market
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 = MRBut p = MR
Why? ∆C/ ∆ y = MC
Choose to produce where MR=MCWhy does this make sense?
Exceptions to the Rule
A= point of minimization Why?
MC downward sloping => increasing y, decreasing mc =>
Decreasing C MR=> increases as y increasesB= point of maximization
A BP*
Df
mc
Y
P
(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 DownShort-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 orCv(y) > pyOr Cv(y)/(y) > p or p < AVC => shutdownSimilarly in the Long Run: = 0 if shutdown
= py – C(y) or p < AC
A= Short Run shut down pointB = Long Run shut down point
A
BAVC
AC
p
Y
$
y
MC
LRAC
A = LR shut-down point
Short Run Supply = portion of MCAbove point A in 1st graphAlso LR Supply = portion of LRMC above LRACloss minimization
A
Profit (graphically)
Also Inverse Supply2 Choices:
(1)Ps = S (y)(2)y= S (P)
P*
AC
Df
p
y
MC
AVC
y*
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
Y
S
P*
y*
Producer surplus
p
YY
Producer Surplus = the shaded area in the graph
Why are the two graphs equivalent?
MC
AVC
ACP*
p
y*
P*
MC
AC
AVC
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 CurveS-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) > 0Or p > c(y)/y or P > ATC
LR Supply
Constant Returns to Scale
y
Lmc
L atc
$
L atc = LmcCmin
y
$
What is LR Supply?
Relationship between long-run and short-run supply curve for a given firm is given by:
p
Y
SSR
SLR
Y1
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 = LR since all inputs are variable.
In the short-run, firms can be found with 3 different situations where y > 0.
P*
AC
Df
p
y
MC
AVC
y*
P*
AC
Df
p
y
MC
AVC
y*
1) π > 0, y > 0 2) π = 0, y > 0
P*
AC
Df
p
y
MC
AVC
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 CompetitionNo 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?
Notice that y* must occur where LRAC is at its minimum. Why?
Also p* = C(y*) => π = 0.
P*
LRAC=AVC
Df
p
y
MC
y*
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:
D1
P*
S3
S2
S4
p
Y
S1
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
D1
P1P*
S3
S2
S4
p
Y
S1
Y1
D2
Y2
With large plants then long-run supply looks like:
P*
S3
S2
S4
p
Y
S1
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
Y
SLR = min LRAC
TaxesThe graph below shows the SLR both before and
after a tax is imposed.
P*
p
Y
SLR before tax
SLR after tax
taxP*+ tax
Where is the equilibrium?For that must have Demand and SSR
P*
p
Y
SLR before tax
SLR after tax
taxP*+ tax
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.
D
SSR SSR
P1
Before assumed that costs were constant with entry. Is that a reasonable assumption?
P*
p
Y
SLR = min LRAC P*
p
Y
SLR = min LRAC
Increasing costs with entry Decreasing costs with entry
Economic RentSuppose that we look at the rent earned by a
highly paid sports or entertainment individual.Do D and S still determine price?
Yes.
P*
p
Y
S
D
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
Y
S
D
P*
p
Y
S
D
Talent Market NoTalent Market
Final notes on Perfect CompetionAssume 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*
p
Y
S=MSC
D=MSB
Y*