Microeconomics: Perfect Competition and Output Decisions at Bocconi University

Microeconomics Course Overview

Università Bocconi
Microeconomics
Prof. Elisa Borghi
&
Prof. Maristella Botticini
2024-2025
T18

1This week and next week:
Lectures T16-T21
After studying production (ch. 19) and costs (ch.
21, 22), we are going to study and compare three
market structures:

• perfect competition (ch. 20, 23, 24; 14, 16)
• monopoly (ch. 25, 26)
• oligopoly (ch. 28 --- Game Theory will be
  back) [BEMACS only]

Perfectly Competitive Markets Introduction

2Chapters 20, 23, 24
Perfectly Competitive Markets
Road Map

1. Profit maximization: general rule
2. Shut-down decision: general rule
3. Perfectly competitive markets
   i. short run
   a) profit maximization
   b) shut-down decision
   c) firm's and market supply functions
   d) producer surplus
   ii. long-run

Firm's Goal: Profit Maximization

Prologue, I: Economic Profit

3Prologue, I
In microeconomic theory, the firm's goal is:
max Tt(q) = R(q) - C(q)
q
where R (q) = revenue
and C (q) = economic cost
Remark 1: It is the extra-profit or economic profit
(different from the accounting profit)
Remark 2: If IT = 0 then there is no extra-profit
All factors obtain the same return as in the best
alternative use.

Prologue, II: Factors Influencing Firm Behavior

4Prologue, II
. How much q should a firm produce to max T?
· The firm has to consider:
1. its cost functions (cost minimization)
2. the market demand
3. its beliefs about how competitors behave
· Firms's behavior depends on market structure
(e.g. perfect competition, monopoly, oligopoly, etc),
which in turn depends on

• number of firms (many, one, few)
• ease of entry/exit
• product differentiation

Profit Maximization: General Rule

Two-Step Process for Profit Maximization

51. Profit maximization (general rule)
· In any market structures, a firm uses a two-step
process to maximize profit:
1. Output decision
Choose the quantity q* that maximizes profit T(q*)
2. Shutdown decision
Compare the profit when producing the optimal
amount q* vs the profit if the firm shuts-down
(q = 0) and exits the market
If (q*) > T(0), the firm continues producing q*
" If TT(q*)

Output Decision: First Order Condition

61.1 Output decision (general rule), I
· The aim of the firm is profit-maximization:
max Tt(q) = R(q) - C(q)
q
· F.O.C. (necessary cond.): Marginal profit = 0
du(q*)
dq
= 0
· S.O.C. (sufficient cond.): Second derivative < 0
(TT(q)
concave function to ensure we have a max!)
dªn(q*)
dq2
12
<0

Output Decision: Marginal Revenue and Cost

71.1. Output decision (general rule), II
max Tt(q) = R(q) - C(q)
q
dTt(q*)
FOC:
=
dR(q*)
−
dC(q*)
= 0
dq
dq
dq
dR(q)
•
= marginal revenue (MR)-> change in
dq
revenue from selling an additional unit of output
dc(q)
•
= marginal cost (MC) -> change in cost
dq
from producing an additional unit of output
FOC: MR(q*) = MC(q*)

Output Decision: Why MR(q*) = MC(q*)

81.1. Output decision (general rule), III
MR(q*) = MC(q*)
Why?
Suppose MR > MC
The additional revenue from an additional unit sold is
larger than the additional cost: producing an additional
unit increases the profit.
Suppose MR < MC
The additional revenue from an additional unit sold is
smaller than the additional cost: reducing production by
one unit increases the profit.

Output Decision: Second Order Condition

91.1 Output decision (general rule), IV
· Second order condition:
d2T(q*)
dq2
<0
dMR(q*)
dq

dMC(q*)
q
· The slope of the MR must be smaller than the slope
of the MC at the optimal level of output q
*

Shutdown Rule: General Case

102. Shutdown rule (general case)
From slide 6:
" if (q*) ≥ T(0), the firm continues producing q*
if TT(q*) GENERAL RULE: the firm shuts down if the revenue is lower
than the avoidable cost.
We distinguish three cases:
If there are no fixed costs, the shutdown rule is:
shut down if R < VC
(or Tt < 0)
If there are fixed costs but they are avoidable if the firm shuts
down, the shutdown rule is:
shut down if R < C (= F+ VC)
(or TT < 0)
If there are fixed costs but they are sunk, and hence, the firm
cannot avoid them even if it shuts down, economic theory tells
the firm: do NOT consider these fixed sunk costs in your
decision on whether to shut down. Then,
shut down if R < VC
(or T < 0)

Perfectly Competitive Markets: Assumptions

113. Perfectly competitive markets
(henceforth, p.c.)

12Perfect competition: assumptions

1. Many symmetric and small firms (price-taking behavior)
   · No single firm's or buyer's actions can raise or lower the price
   · Individual firm's demand curve is a horizontal line at the market price
2. Identical (homogeneous) products
   · If all firms are selling identical products, it is difficult for any firm to
   raise the price above the going market price charged by all firms
3. Full information
   · Consumer knowledge of all firms' prices makes it easy for consumers
   to buy elsewhere if any one firm raised its price above market price
4. Negligible transaction costs
   · Buyers and sellers waste little time or money finding each other
5. Free entry and exit in the long run
   · When firms in the market make profits: entry
   · When firms in the market make losses: exit
   · Free entry/exit ensures a large number of firms in the market and
   promotes price-taking behavior

Why Study Perfectly Competitive Markets

13Perfectly competitive markets:
why we study them
· The assumptions that characterize perfectly
competitive markets are quite strong.
· Question: are perfectly competitive markets
realistic? why do we study them even though the
assumptions are strong?
· Answers:
- some markets have a similar structure
- total (consumers' and firms') welfare is
maximized
- useful benchmark to compare other market
structures

Price Taking in Perfect Competition

Price Taking, I: Information and Strategy

14Perfect competition:
Price taking, I
· In perfectly competitive markets, buyers
and sellers are price takers
- The price conveys all the information
needed by the firm about demand and
competitors' behavior
-> No strategic interactions among firms

Price Taking, II: Horizontal Demand Curve

15Price taking, II
· If a firm is price taker, then it faces a horizontal
demand curve, (||| > 00) (demand curve for the
individual firm)
- if the firm sets a price higher than the market price,
it loses all the customers
- the firm can sell as much as it wants at the market
price, thus it has no incentive to lower its price
· Buyers are price takers too:
- a consumer is unable to purchase at a price less
than the market price

Firm's Demand Curve in Perfect Competition

16Perfect competition: firm's demand curve
· Is a perfectly competitive firm's individual demand curve
really flat?
· A firm's residual demand curve, D' (p), is the portion of
the market demand that is not met by other sellers at any
given price
Di (p) = demand faced by the individual firm
D(p) = market demand
Sº(p)= amount supplied by other firms
Di(p) = D(p) - Sº(p)
· If not perfectly horizontal, the residual demand curve of
an individual firm is much flatter than the market demand.

Perfect Competition in the Short Run

Output Decision: Analytical Approach

173.i Perfect competition in the short run:
Output decision, analytically
In p.c. firms are price taker: the price does not depend on
the amount sold by the individual firm. That is, p(q) = p
· Hence, firm's revenue R (q) = p . q
which implies MR(q) = p ! (only in p.c. this happens!)
· FOC: MR(q ) = MC (q) = p = MC(q*)
dMR(q)
dMC(q)
⇒
dMC(q)
dq
> 0
· SOC:
dq
dq
which means that the marginal cost must be upward
sloping at the profit-maximizing quantity q
*

Output Decision: Graphical Representation I

18Perfect competition in the short run:
Output decision: graphically, I
p
MC
When MC is U-shaped:
MR = MC in two points!
AC
SOC: q* (max profit) is
on the upward sloping
MR = p part of MC.
To max n, the firm
produces q*
q
*
q

Output Decision: Graphical Representation II

19Perfect competition in the short run:
Output decision: graphically, II
d
MC
AC
MR = p
*
AC(q
q
*
q
q* is the profit
maximizing quantity
Revenues = p . q*
(blue area)
Cost = AC (q*) · q*
(red area)
Profit = R (q*) - C (q*)
(green area)

Shutdown Decision in the Short Run

20Competition in the short run:
Shutdown decision
· A competitive firm shuts down if the market price
is smaller than the minimum of its short-run
average variable cost curve
- In the short run, the firm may decide to produce
even when profit is negative, if this implies that
the firm reduces its loss.
· Shutdown rule
- the firm produces if p ≥ min AV C
- the firm shuts down if p < min AVC

Shutdown Decision, I: Positive Profits

21Competition in the short run:
Shutdown decision, I
d
MC
P
TT > 0
AC
Min AC
AVC
Min AVC
q
*
q
CASE 1
If p > min AC
Then
TT > 0 => q* > 0
Positive profits:
the firm operates!

Shutdown Decision, II: Operating with Losses

22Competition in the short run:
Shutdown decision, II
d
MC
AC
Min AC
TT ≤ 0
AVC
p
Min AVC
*
q
q
CASE 2
If min AVC < p < min AC
Then, T < 0!
However, the firm operates,
because the loss is lower than
the fixed cost F.
If the firm decides to exit the
market, it will lose the sunk
fixed cost F.
In this case the revenue is
covering all the variable cost
and part of the fixed cost
q* > 0!

Shutdown Decision, III: Shutting Down

23Competition in the short run:
Shutdown decision, III
d
MC
AC
F
Min AC
AVC
TT ≤ 0
Min AVC
P
q®
*
q
CASE 3
If p < min AVC
Then
T < 0 and I < - F!
Negative profit!
The firm shuts down.
The firm's revenue is less
than its variable cost, so it
makes a greater loss by
operating than by shutting
down, because it loses
money on each unit sold in
addition to the fixed cost.

Short-Run Firm's Supply Function

24Short-run firm's supply function
· Having analyzed the output decision and
the shutdown decision of a competitive
firm in the short run, we can derive the
firm's supply function --- crucial concept!
· Definition: the competitive firm's short-run
supply function is the quantity supplied as
a function of the market price.

Firm's Supply Curve in Short-Run Competition

25Competition in the short run:
the firm's supply curve
d
MC
AC
AVC
Min AVC
q
If p < min AVC
the firm shuts down:
q : q* = 0
If p ≥ min AVC
the firm operates and
sets q* to maximize Tt:
qi : p = MC (q*)
Firm's short run
supply curve!

Short-Run Firm Supply Function: Analytical View

26Short-run firm supply function,
analytically
if p < min AV Ci (q)
0
913: p=
p = MCi(q)
if p > min AV Ci (q)

Short-Run Market Supply Function

Market Supply Function, I: Horizontal Sum

27Short-run market supply function, I
· The short-run market supply curve is the
horizontal sum of the individual firms' supply
curves.
. In the short run the number of firms n is fixed,
as new firms need time to enter the market.

Market Supply Function, II: Identical Firms

28Short-run market supply function, II
· Identical firms: same shutdown price!
Qs =
n · qi
S
if p < min AV Ci
if p ≥ min AV Ci
· The larger n , the flatter the market
supply curve is.

Market Supply Function, III: Graphical Example

29Short-run market supply function, III
· Identical firms: same shutdown price!
(a) Firm
(b) Market
p, $ per ton
7
S1
6.47
AVC
6
5
T MC :
0
50
140 175
q, Thousand metric tons
of lime per year
p, $ per ton
7
S2
S3
S4
6.47
S5
6
5
0
50
150 250
200
700
100
Q, Thousand metric tons
of lime per year

Market Demand and Equilibrium

30.... let's bring the demand side in ...
Before analyzing the short-run and long-run
individual firm's equilibrium in competitive
markets, we need to go back to chapters 14,
15 and 16 (in a selective way) and introduce
the market demand function and analyze
the competitive market equilibrium.
So, let's switch slides ...!
... when we are done, we can come back here
and move to the next slide in this lecture.

31