Download Short Run Equilibrium

Review
The supply function:
1. The individual firm’s supply is calculated in two steps:
First, we figure out whether the firm produces or shuts down, is the price greater than the shutdown
price?
Second, if the firm produces, how much? (given by the mc(q)=p)
2. The total market supply is the sum of the amount supplied by each individual firm
Useful remember:
A firm that maximizes profits always produces at point where mc(q)=p, the firm makes
profits if ATC(q)>p and the firm loses money if ATC(q)<p
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.
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.
Long Run Equilibrium
Question: What happens in the long run?
The long run differs from the short run in two key ways:
1. Firms can adjust all inputs and there are no sunk costs.
2. There is entry and exit: the number of firms in the industry can change as well. A firm
that suffer loses can leave the market, and a firm that anticipates gains can enter.
Long Run Equilibrium
Since there are no sunk costs, the firm shuts down if p<minATC(Q) = Ps, and
the supply is given by:
P = MC(Q) for P > Ps and the firm exits if P < Ps
Long Run Equilibrium
Key definition:
A long run equilibrium is a price P*, quantity Q* and number of firms n, such that:
1. Individual firms maximize profits, each firm produces q* such that: P*=mc(q*)
2. Markets clear, market demand equals market supply, Qd(P*) = Q* = Qs(P*)
Where the aggregate supply Qs(P*)=nq*
3. No firm wants to exit or enter. This implies that firms must not be making profits
or suffering loses: Zero profits
The difference from the short run is the zero profit condition. It relies on the assumptions
that firms can exit, so no losses are incurred, and there are always firms that can enter, so no
profits can be gained. Why?
Long Run Equilibrium
Key Property:
The zero profit condition implies that in the long run each firm is producing a quantity q
such that ATC(q) is at the minimum point. Why?
i. If p<ATC(q) firms exit and the market price will rise (why?). If p>ATC(q) there are profits, firms will
enter and the market price will fall (why?). Thus p=ATC(q)
ii. Since each firm is maximizing profits, each firm chooses a quantity q such that mc(q)=P.
The only quantity level where mc(q)=p=ATC(q) is the minimum of the ATC curve.
$/unit
$/unit
MC
ATC
Market demand
q
q
Long Run Equilibrium
Key Property:
In the long run, the market price p and each individual firm’s output q, must be such that:
mc(q)=P=ATC(q),
$/unit
$/unit
MC
Market demand
ATC
p
q
q
Q*
Q
Long Run Equilibrium
Example: Suppose a certain market has the following demand function: Qd(P) =
25000-1000P. Firms have the cost function TC(q) = 40q - q2 + .01q3. What is the
market equilibrium?
We solve this in three steps:
1. Calculate the individual firm’s optimal output level and then get the market price.
From zero profits: ATC(q)=P and from profit maximization, mc(q)=p. Together, ATC(q)=mc(q),
and we can solve for q. AC(q) = 40 – q + .01q2 and MC(q) = 40 – 2q + .03q2
And we have that q* = 50 the price is P* = 15
2. Calculate the market quantity. Since the price is P* = 15, from the market demand we
can calculate the market quantity: Qd(P) = 25000-1000P, and Qd(15)= 10,000
3. Calculate the number of firms. Given the market quantity, and the individual firm’s quantity
produced we can calculate the number of firms: nq*=Q*,
and since total output Q*=10,000 and each firm produces q*=50 units, there must be
n=10,000/50=200 firms.
Long Run Equilibrium
Difference in calculating long and short run equilibrium
Long Run
Short Run
Step 1: Individual firm’s
output
mc(q)=ATC(q)=p
mc(q)=p
Step 2: Market quantity
Use Price from step 1
and market demand to
calculate the market
quantity
Calculate market supply,
use market clearing
condition to get price
and quantity
Step 3: Number of firms
Calculate the number of
firm’s
Number of firms is
given. Calculate
individual firm’s output
Long Run Supply Curve
Definition: The Long Run Market Supply Curve maps the quantity of output supplied
for each given price. The supply of firms takes place after all long run adjustments of
inputs, and entry or exit of firms.
The zero profit condition pins down
the long run supply.
SRS
p
P0
LRATC=LRS
D
Q
Q0
Output expansion or contraction in
the industry occurs along a
horizontal line corresponding to the
minimum level of long run average
cost.
Long Run Market Dynamics
Example of industry dynamics The Super Tanker Industry
Super Tankers are large ships used for transport (usually oil). A super tanker can cost
around $100 million.
In the 60s and early 70s, the demand for Tankers was high, mainly driven by the high
demand for oil, 500 new super Tankers were constructed. But in the 70s prices for service
of Tankers collapsed, due to the oil embargo. Short run supply is inelastic, as Tankers have
no alternative value. It took years for the industry to adjust. In 1978, over 20 million tons
worth of tanker capacity was sold for scrap.
Long Run Market Dynamics
In general, the long run dynamics of prices are shaped by supply side
effects (such as economies of scale) and demand side effects (such as
network externalities – think of cell phones).
For example, the revenue cycle of computer memory chips (DRAM)
$50
$40
$30
$20
$10
$0
1992
Question:
What causes such price
cycles?
1994
1996
1998
2000
2002
2004
Long Run Market Dynamics
We know how a single firm responds to a shift in input
prices, or market price.
The next goal is to understand how prices in a competitive
market responds to a change in demand
Long Run Market Dynamics
Suppose demand increases
SRS
P
Initially market price increase, and
output increases.
P1
What happens next?
P0
LRATC=LRS
D1
D0
Q
Q0
Q1
Long Run Market Dynamics
Suppose demand increases
SRS0
P
SRS2
P1
P0
Since prices rise, p>ATC, and each
firm earns a profit. Leads to entry
and an increase in supply.
LRATC=LRS
D1
D0
Q
Q0
Q1
Q2
In the new equilibrium:
- Price decreases to the original
price
- Output further increases.
- The number of firms increase.
Long Run Market Dynamics
Suppose demand decreases
P
SRS2
Initially market price decreases, and
output decreases.
SRS0
What happens next?
LRS
D1
D0
Q
Since prices fall, p<ATC, each firm
suffers a loss. Leads to exit and a
further decrease in supply.
In the new equilibrium:
- Price rise to the original price
- Output further decreases.
- The number of firms decreases.
Long Run Market Dynamics
The previous analysis made two simplifying assumptions:
1.
2.
As the number of firms increases, the costs of each individual firm
do not change
As prices change, consumers do not change their behavior
Long Run Market Dynamics
Key definition
1.
In a constant-cost Industry an increase in industry output does not
affect the prices of inputs.
2.
In an increasing-cost Industry an increase in industry output increases
the prices of inputs.
3.
In a decreasing-cost Industry an increase in industry output decreases
the prices of inputs.
Long Run Market Dynamics
Increasing-cost Industry: an increase in demand
Step 1 Initial effect: prices rise.
Since prices fall, p>ATC, each firm
makes a profit in the short run.
Leads to entry.
Step 2 Entry has two effects:
i.
ii.
Industry supply increases
Individual firm’s costs increase
In the new equilibrium:
- Price rise above the original
price
- Output increases.
- Number of firms increases
- Average total costs are
higher
Long Run Market Dynamics
Decreasing-cost Industry: an increase in demand
Step 1 Initial effect: prices rise.
Since prices fall, p>ATC, each firm
makes a profit in the short run.
Leads to entry.
Step 2 Entry has two effects:
i.
ii.
Industry supply increases
Individual firm’s costs decreases
In the new equilibrium:
- Price fall bellow the original
price
- Output increases.
- Number of firms increases
- Average total costs are
lower
Long Run Supply Curve
Definition:
The Long Run Market Supply Curve maps the quantity of output supplied for each
given price. The supply of firms takes place after all long run adjustments of inputs, and
entry or exit of firms.
Long Run Market Dynamics
1.
In a constant-cost Industry long run supply is horizontal
2.
In an increasing-cost Industry long run supply increases
3.
In a decreasing-cost Industry long run supply decreases
Long Run Market Dynamics
Example of increasing cost industry: The US Ethanol market
Ethanol is a liquid produced (mostly) from corn, and can be used to produce, amongst
other things, bio-fuel.
In 2000s there was a sharp increase in demand, increasing prices.
As the industry grew, the price of corn rose sharply, increasing the production costs
As a result, the number of new plants fell sharply
Long Run Market Dynamics
Example of increasing cost industry: The computer memory market
1. Most costs are fixed (expensive plants, low production costs), leads to vertical short
run supply curves
2. Economies of scale costs have decreases 30% per year
3. Demand adjust dynamically toward a long run equilibrium
P
0
2
$50
$40
$30
$20
$10
$0
1
SRS0
SRS1
SRD0 SRD
2
1992
LRD
LRS
Q
1994
1996
1998
2000
2002
2004
Producer Surplus
Difference between surplus and profit
If a firm produces with better inputs it generates a surplus.
Producer Surplus
Definitions
•
The reservation value is the return that the owner of an input could get by deploying the
input in its best alternative use outside the industry.
The economic rent that is the difference between the maximum value that a firm is willing
to pay for the services of the input and input’s reservation value.
Producer Surplus
Definition:
Producer Surplus is the area above the market supply curve and below
the market price. It is a monetary measure of the benefit that producers or other input
suppliers derive from producing a good and selling it at particular price.
P
Market Supply Curve
P*
Producer Surplus