P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
1
Page 1
Perfect Comp. with Exit/Entry & Quantity Choice
Based on the blackboard in Session 4 and slides in Session 5:
merged, filled in, and streamlined.
2
Main ideas: each firm
Each firm has a break-even price, above which it would enter or stay in the
market, below which it would exit or stay out of the market.
Because of economies of scale, firm has a minimum scale of production:
entry is a discrete jump into the market.
These things were true in entry/exit with fixed quantity. But there,
break-even price and scale were given to us. Here we need to calculate
them taking into account quantity choice. We also need to find the actual
quantity produced when price exceeds break-even.
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
3
Main ideas: aggregate supply
Page 2
(could look like this)
P
30
25
Aggregate
supply
20
15
10
5
0
Q
0
50
100
150
200
250
300
350
A flat part shows entry of a firm. It occurs at the firm’s break-even price on the vertical axis. Its
width on the horizontal axis is the scale with which the firm enters the market.
Between these flat parts, there is no entry. But existing firms expand output as the price rises.
4
Main ideas: equilibrium
P
30
25
Aggregate
supply
20
15
10
Demand
5
0
Q
0
50
100
150
200
250
300
350
Supply=Demand determines how many firms are in the market and how much each produces.
Here there are 5 firms in the market.
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
5
Perfect Comp. with Exit/Entry & Quantity Choice
Each firm’s entry/exit and quantity decisions
➥ 1. Its about AC & MC
2. Numerical example
Aggregate supply and equilibrium
3. Diverse firms
4. Identical firms (free entry)
6
Quantity decision depends only on the MC curve
€
MC
8
7
P 6
5
4
3
2
1
10
20
30
40
s(P)
50
60
70
Q
Page 3
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
7
Entry/exit: It is about average cost
Average cost speaks about:
• economies of scale
• entry and exit decisions.
8
Typical AC curve: U-shaped
(Could be more complicated, but U-shaped AC provides best intuition.
It is only case we consider with perfect competition.)
€
8
7
AC
6
5
4
3
Decreasing AC
= Economies of scale
Increasing AC
= Diseconomies of scale
2
1
10
20
30
40
50
60
70
Q
Page 4
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
Page 5
Economies of scale
9
Economies of scale come from:
(a) long-run fixed costs (= entry costs, set up costs, first-copy costs, …)
(b) returns to specialization
(c) use of different technologies and indivisible inputs at different scales
These translate into decreasing MC, or more complicated patterns.
FC > 0 . Simplest case. Best intuition. Only case we consider.
So, for us: U-shaped AC means FC > 0 and increasing MC.
10
Profit > 0 ⇔ P > AC
AC and profitability:
€
8
7
AC
P 6
5
4
3
Loss
Loss
Profit
2
1
10
20
30
40
50
60
P = 5.8 : some quantities lead to profit, others a loss.
P=4
: it is impossible to earn a profit.
70
Q
(Need MC curve to see which
quantity gives highest profit.)
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
11
Page 6
Min AC = break-even price = entry/exit threshold
Price:
€
8
Enter
or
stay in
7
AC
6
ACu 5
4
Exit
or
stay out
3
2
1
10
20
Q
12
u
30
40
50
60
Q
70
Combine to see entry and scale decisions at same time
Produce nothing until P ≥ ACu . Then enter market with Q u .
Always produce at least Q u , following MC curve.
€
MC
8
7
AC
6
ACu 5
4
3
2
1
10
20
Q
u
30
40
50
60
70
Q
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
13
Perfect Comp. with Exit/Entry & Quantity Choice
Each firm’s entry/exit and quantity decisions
✓ 1. Its about AC & MC
➥ 2. Numerical example
Aggregate supply and equilibrium
3. Diverse firms
4. Identical firms (free entry)
14
Exercise 3.8
TC = 144 + 3Q + Q 2
FC = 144
MC = 3 + 2Q
AC =
144
+3+Q
Q
constant/intercept
derivative
TC /Q
Q u = 12
solves MC = AC
ACu = 27
= ac(Q u ) = mc(Q u )
Page 7
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
15
Page 8
MC = 3 + 2Q
€
MC
50
40
30
20
10
5
16
144
Q
AC =
10
15
20
25
Q u = 12
+3+Q
Q
30
AC u = 27
€
50
40
ACu
AC
30
20
10
5
10
Q
u
15
20
25
30
Q
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
17
Page 9
Together
€
MC
50
40
ACu
AC
30
20
10
5
18
10
Qu
15
20
25
30
Q
Perfect Comp. with Exit/Entry & Quantity Choice
Each firm’s entry/exit and quantity decisions
✓ 1. Its about AC & MC
✓ 2. Numerical example
Aggregate supply and equilibrium
➥ 3. Diverse firms
4. Identical firms (free entry)
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
19
Page 10
Numerical example too complicated;
just understand interpretation.
Aggregate supply
P
30
25
Aggregate
supply
20
15
10
5
0
Q
0
50
100
150
200
250
300
350
A flat part shows entry of a firm. It occurs at the firm’s break-even price ACu on the vertical
axis. Its width on the horizontal axis is the scale Q u with which the firm enters the market.
Between these flat parts, there is no entry. But existing firms expand output as the price rises,
following their MC curves.
20
Numerical example too complicated.
Just understand interpretation.
Equilibrium
P
30
25
Aggregate
supply
20
15
10
Demand
5
0
Q
0
50
100
150
200
250
300
350
Supply=Demand determines how many firms are in the market and how much each produces.
Here there are 5 firms in the market. Their total output comes from MC=P.
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
21
Page 11
Equilibrium profit
P
30
25
Aggregate
supply
20
15
10
Demand
5
0
Q
0
50
100
150
200
250
300
350
Usual shading of producer/consumer surplus works.
Compared to entry/exit with fixed quantity, we cannot identify profit of individual firm.
Still, a firm is in the market and earns profit because of cost advantage over other firms.
22
Long-run adjustment to shift in demand
P
30
25
Aggregate
supply
20
15
10
New demand
5
0
Q
0
50
100
150
200
250
300
350
Shift in demand leads to higher price and output, as usual.
Here, higher output comes from entry of one more firm and expansion of output by all firms.
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
23
Page 12
Perfect Comp. with Exit/Entry & Quantity Choice
Each firm’s entry/exit and quantity decisions
✓ 1. Its about AC & MC
✓ 2. Numerical example
Aggregate supply and equilibrium
✓ 3. Diverse firms
➥ 4. Identical firms (free entry)
24
Main ideas are same as
when quantity is fixed
Similar firms (almost free entry)
P
30
Aggregate
supply
25
20
15
10
Demand
5
0
Q
0
50
100
150
200
250
300
350
Firms have similar break-even prices; these nearly pin down equilibrium price.
Supply is very elastic: small changes in price ⇒ big change in number of firms.
Each firm in the market has low profit.
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
25
Page 13
Main ideas are same as
when quantity is fixed
Identical firms (free entry)
P
30
25
ACu
Aggregate
supply
20
15
10
Demand
5
0
Q
0
50
100
150
200
250
300
350
Firms have same break-even price ACu ; this pins down equilibrium price.
Supply is perfectly elastic.
Each firm has zero profit.
26
Identical firms: Calculations
When we studied free entry with fixed quantity,
the break-even price and quantity per firm were given.
Now we calculate them from the AC curve. Otherwise, same logic.
1. P ∗ = ACu
[Common break-even price]
2. Q ∗i = Q u
[Common minimum scale]
3. Q ∗ = d (P ∗ )
4. N ∗ = Q ∗ /Q ∗i
[From the demand curve]
[Total output divided by output per firm]
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 4 • Entry/Exit with Quantity Decision [Summary]
Page 14
Example
27
—— Each firm
TC = 144 + 3Q + Q 2
——
—— Market ——
€
€
MC
Demand: Q = 510 - 10P
FC = 144
40
AC
MC = 3 + 2Q
AC =
144
+3+Q
Q
40
P∗ =
ACu
ACu
20
Agg. supply
20
Q u = 12
ACu = 27
Qi
10
28
Qu
20
30
100
200
Q∗
1. P ∗ = 27
3. Q ∗ = d (27) = 240
2. Q ∗i = 12
4. N ∗ = 240 ÷ 12 = 20
300
Perfect Comp. with Exit/Entry & Quantity Choice
Each firm’s entry/exit and quantity decisions
✓ 1. Its about AC & MC
✓ 2. Numerical example
Aggregate supply and equilibrium
✓ 3. Diverse firms
✓ 4. Identical firms (free entry)
400
500
Q