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*