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 S 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 = MR But p = MR Why? ∆C/ ∆ y = MC Choose to produce where MR=MC Why 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 increases B= point of  maximization A B P* 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

2 nd 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 shutdown Similarly in the Long Run:  = 0 if shutdown  = py – C(y) or p < AC

A= Short Run shut down point B = Long Run shut down point A B AVC AC p Y

$ y MC LRAC  A = LR shut-down point Short Run Supply = portion of MC Above point A in 1 st graph Also LR Supply = portion of LRMC above LRAC loss minimization A

Profit (graphically) Also Inverse Supply 2 Choices: (1)P s = 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 Y Y Producer Surplus = the shaded area in the graph Why are the two graphs equivalent? MC AVC AC P* 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 Curve S-R Supply Curve = MC above AVC Where MR=MCP= 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 LR Supply Constant Returns to Scale y Lmc L atc $ L atc = Lmc Cmin y $ What is LR Supply?

Relationship between long-run and short-run supply curve for a given firm is given by: p Y S SR S LR Y1Y1

Why would S LR be more elastic (more responsive to price changes)? Can change both K & L optimally in the L-R => Increase y at lower cost beyond y 1 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 > 02) π = 0, y > 0

P* AC Df p y MC AVC y* 3) π 0; why is y>0? What is the short-run industry supply? S = Σ S i (P) = Σ MC i 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 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 MC i = nMC; where i=n (i.e., n = the the total number of firms. Suppose that there are 4 possible firms then get: D1D1 P* S3S3 S2S2 S4S4 p Y S1S1

Notice that equilibrium p and y is given by the lowest possible price where p 1 ≥ p* and y* is at that intersection. Thus, if D = D 1 then p = p 1 and Y = Y 1 If D = D 2 the p = p 1 and Y = Y 2 D1D1 P1 P* S3S3 S2S2 S4S4 p Y S1S1 Y1Y1 D2D2 Y2Y2

With large plants then long-run supply looks like: P* S3S3 S2S2 S4S4 p Y S1S1 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 S LR = min LRAC

Taxes The graph below shows the S LR both before and after a tax is imposed. P* p Y S LR before tax S LR after tax tax P*+ tax

Where is the equilibrium? For that must have Demand and S SR P* p Y S LR before tax S LR after tax tax P*+ 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 S SR P1P1

Before assumed that costs were constant with entry. Is that a reasonable assumption? P* p Y S LR = min LRAC P* p Y S LR = min LRAC Increasing costs with entryDecreasing 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* 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 MarketNoTalent 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* p Y S=MSC D=MSB Y*