Perfectly Competitive Market
Topics:
1. Definition of a Perfectly Competitive Market
2.Short Run Equilibrium
3. Long Run Equilibrium
Perfectly Competitive Market
Key definition: A perfectly competitive market satisfies the following conditions:
1. Fragmented industry consists of many small buyers and sellers
2. Buyers and Sellers are “price takers”:
- Each buyer’s purchases are small and do not effect the market price
- Each seller is small and does not effect the market price
-Each seller cannot effect the price of inputs
3. Firms produce identical products
4. Perfect information about prices
5. All firms have the equal access to inputs, they have the same technology,
and there is free entry. Implies that firms have identical long run cost
functions
Perfectly Competitive Market
The Law of One Price: Since products are identical and there is perfect
information, there is a single price at which transactions occur.
A firm takes the price as given and chooses Q to maximize profit.
The firm’s problem
max pQ  TC (Q)
Q
s.t.Q  0
Optimality condition: P = MC(Q)
The Firm’s Decision
Does the firm choose to produce a positive quantity Q>0 or to shut down and produce nothing
Q=0?
The Firm’s Decision
The firm’s problem
max  (Q)  TR (Q)  TC (Q)
Q
- The Marginal Revenue is 𝑀𝑅 𝑄 =
∆𝑇𝑅(𝑄)
∆𝑄
: the additional revenue generated if the firm increases output by an additional
“small” unit
- The Marginal Cost is 𝑀𝐶 𝑄 =
∆𝑇𝐶(𝑄)
∆𝑄
: the additional cost incurred if the firm increases output by an additional “small” unit
Optimality condition: If MR(Q)> MC(Q), the firm’s profit increases if it produces more output. If MR(Q) < MC(Q), the
firm’s profit falls if it produces more output.
 The profit maximization condition is MR(Q) = MC(Q)
 Since the firm is a price taker: p=MR(Q)=MC(Q)
 We must also check the shut-down condition: p>MinAVC(Q)
Profit Maximization
Optimality condition:
1. P = MC(Q)
2. MC(Q) increases
Short Run Supply
Example. A firm has the cost function TC(Q) = 100 + 20Q + Q2 and can sell each
unit for a price of 30. How many units will it sell? What is the profit?


Calculate the firm’s profit if the market price is 40, 20, 15.
Derive the firm’s supply.
Short Run Supply
A firm has the cost function TC(Q) = 100 + 20Q + Q2





TFC = 100
ATC(Q)=100/Q+20+Q
TVC(q) = 20Q + Q2
AVC(q) = 20 + Q
MC(q) = 20 + 2Q
The firm’s short run supply curve is:
- If the price is P < 20: then the firm produces nothing Q = 0
- If price is P > 20: then P = MC(Q)  P = 20+2Q  Q = 10 + ½P
Short Run Supply
Key Definition: A single firm’s Short run supply curve specifies the profit maximizing
output for each market price.
The firm’s short run supply curve is give by:
1. When P < Ps the firm chooses to produce nothing, Q=0
2. When P > Ps the firm chooses to produce Q>0 such that MC(Q)=p
$
Fixed costs are sunk:
SMC
ATC
AVC
Ps
Quantity
Short Run Supply
Important to remember: if the firm produces output Q and sells it for a price p then;
1. When p>ATC(Q) the firm makes a profit. When p<ATC(Q) the firm loses money
2. When p>AVC(Q) the firm produces Q>0, when p<AVC(Q) the firm shuts down
(assuming all fixed costs are sunk)
3. When AVC(Q)<p<ATC(Q) the firm operates at a loss
Short Run Market Supply Curve
Definition: The short run market supply is the sum of the quantities each firm
supplies at that price.
Example: suppose 3 types of firms with different marginal costs and different shut down
prices. Each firm has a different
Short Run Equilibrium
Definition: A short run equilibrium is a pair of price and quantity (Q,P) such
that:
1.
2.
Each producer maximizes profits given price p
Markets clear
n
Q   Qsi ( P)  Qd ( P)
i 1
Where Qsi(P) is firm i’s individual profit maximization output given price P.
Short Run Equilibrium
Graphic depiction of a short run equilibrium
Short Run Equilibrium
Graphic depiction of a short run equilibrium
Typical firm produces Q* where MR=MC and if 100 firms make up the
market then market supply must equal 100Q*
Short Run Equilibrium
Example
Suppose a market consists of 300 identical firms, all with the same cost curve:
TC(q)= 0.1 + 150q2. Consumers demand is given by Qd(P) = 60 – P. What is the equilibrium
price and quantity? Do firms make positive profits at the market equilibrium?
Step 1: Derive individual supply curve
FC=0.1 (all are sunk, NSC= 0) ; AVC(q) = 150q; MC(q)=300q
Since min{AVC(q)}=0, the firm always produces.
The profit maximizing condition: MC(q)=MR(q), we have that 300q=p, or qs(P) = P/300 .
Step 2: derive the market supply curve
Qs(P) = 300 qs(P) =300(P/300) = P
Step 3: solve for equilibrium
Qs(P)= Qd(P) or P= 60 – P and
P*= 30, Q* = 30 and each firm produces q* = 30/300=.1
Short Run Equilibrium
Example
Do firms make positive profits at the market equilibrium?
Condition for positive profits: p* >ATC(q*)
ATC (q)= TC(q)/q = 0.1/q + 150q.
Since each firm produces q* = 0.1, we have that ATC(q*)=15<30= p*,
Therefore P* > ATC(q*) and profits are positive
The profit of each firm is: Pq-TC(q)= 30*0.1-(0.1+150*0.1^2)=1.4
Short Run Equilibrium
Example
What happens when the number of firms increases from 300 to 500?
The single firm’s supply is unchanged: mc(q)=P and qs(P) = P/300
But now, market supply increases to Q(P)=400* (P/300) and for markets to clear
we have that :
500* (P/300)= 60 – P or P=22.5 and Q= 37.5 and the individual firm produces q=
37.5/500=0.075
Does each firm make earn a profit? Condition for positive profits: p* >ATC(q*);
ATC (q)= 0.1/q + 150q= 0.1/0.075+150*0.075 =11.25 < 22.5
The profit of each firm Pq-TC(q)= 22.5*0.075-(0.1+150*0.075^2)=1.3
Short Run Equilibrium
Comparative Statics
What happens when the number of firms increase?
Market supply is increased, prices drop, and each firm produces less.