STAT0001: Economics 2 (Combined
Studies)
Alex Donov
Department of Statistical Science
University College London
a.donov@ucl.ac.uk
2Outline: Term 1
• Mathematics Overview and Budget Constraint
• Preferences and Utility
• Choice and Demand
• Revealed Preference
• Slutsky Equation
• Choice under Uncertainty
• Consumer Surplus
• Production Technology and Profit Maximisation
• Cost Minimisation and Cost Curves
• Competitive Markets
3Competitive Markets
• Profit Maximisation Re-Visited
• Perfect Competition Supply
• Short-Run Industry Equilibrium
• Long-Run Entry
4Producer’s Profit-Maximisation
Problem
• Still assuming a price-taking firm but with the cost function from the
cost-minimisation problem
• Assume that is a convex function of y( )yc
( )ycpy
y
−max
5Competitive Markets
• Profit Maximisation Re-Visited
• Perfect Competition Supply
• Short-Run Industry Equilibrium
• Long-Run Entry
6Firm’s Supply Function
• The FONC for the firm’s profit-maximisation
problem is:
– Verify the SOSC:
• Can show that the supply function is the portion of
the MC curve that lies above the AVC
• Furthermore, the supply function is non-decreasing
in the price
( )( ) 0* =− pycp
( )( ) ( )
( )
( )( )
0
1
01
*
*
*
*


=
=−
pycdp
pdy
dp
pdy
pyc
( )( ) ( )( ) 00 ** − pycpyc
7Competitive Markets
• Profit Maximisation Re-Visited
• Perfect Competition Supply
• Short-Run Industry Equilibrium
• Long-Run Entry
8Aggregating Supply
• Suppose that you have N firms in a perfectly
competitive industry
• Firm n solves its profit-maximisation problem
assuming no influence on the market-clearing price
– FONC for firm n:
• In equilibrium, industry supply has to equal the
demand
• Thus, there are N+1 equations and unknowns
( ) ( )pDpy
N
n
n =
=1
*
( )( )pycp nn *=
9Market Equilibrium: Two Asymmetric
Firms, Linear MC, and Linear Demand
( ) ( ) ( )
( ) ( )
( )
( ) ( )
14
20
,
7
20
,
7
20
10
2
7
210
2
3
210
2
210
2
,2,
210,,
2
1
**
2
**
1
*
*
*
*
*
*
*
*
2
1
**
*
2
*
121
2
222
2
111
===
=
−=
−=+
−=
====
−===

=
pypyp
p
p
p
p
p
p
ppyMCC
p
pyppyypypFONC
ppDyycyyc
n
n
10
Market Equilibrium: N Symmetric
Firms, Linear MC, and Linear Demand
( ) ( )
( )
( )
( )
( ) ( )
NB
AN
py
NB
A
py
NB
A
p
ApNB
BpANp
BpApyMCC
ppyypFONC
BpApDyyc
N
n
nn
N
n
n
nn
nnn
+
=
+
=
+
=
=+
−=
−=
==
−==


=
=
1
*****
*
**
*
1
**
*
2
,,
,
2
1
11
Comparative Statics: N Symmetric
Firms, Generic MC, and Generic
Demand
( ) ( ) ( )
( ) ( ) ( )
( )( ) ( )( )
( )( ) ( )( )
( )( ) ( )( ) ( ) ( )( ) ( )
( ) ( )( )
( )( ) ( )( )
0
,
***
***
*****
**
***
*
1
**
**

−
=
=+
=
=
==
=

=
dp
Npdy
N
dp
NpdD
Npy
dN
Ndp
dN
Ndp
dp
NpdD
dN
Ndp
dp
Npdy
NNpy
NpDNpNy
NpDNpyMCC
pypyycpFONC
pDnycyc
N
n
nn
nnn
12
Welfare Analysis: Two Asymmetric
Firms, Linear MC, and Linear Demand
( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( )
( )
7
10
,
7
20
02
2
52
0
2
51
4
5max
max
210,,
2
1
*
2
*
1
*
2
*
2
*
1
*
1
*
2
*
1
*
22
*
11
2*
2
*
1*
2
*
1
,
2
1
*****
0,
2
222
2
111
*
2
*
1
*
*
2
*
1
==
=−
+
−
=−
+
−
−−
+
−+
−+−=+=
−===

=
yy
y
yy
FONC
y
yy
FONC
ycyc
yy
yy
ycYpYpdYYpPSCSSW
ppDyycyyc
yy
n
nn
Y
D
yy
13
Welfare Analysis: N Symmetric Firms,
Linear MC, and Linear Demand
( ) ( )
( ) ( )
( ) ( )
( )
NB
A
y
B
AN
B
NBN
y
Nyy
B
N
B
AN
FONC
yNcy
B
N
y
B
AN
ycYpYpdYYpPSCSSW
BpApDyyc
y
N
n
nn
Y
D
yy
nnn
N
+
=
=
+

=−−
−−
−+−=+=
−==

=
*
*
**
2
*2*
2
*
1
*****
0,,
2
0
2
max
max
,
2
1
*
*
**
1 
14
Competitive Markets
• Profit Maximisation Re-Visited
• Perfect Competition Supply
• Short-Run Industry Equilibrium
• Long-Run Entry
15
Long-Run Perfectly Competitive
Equilibrium
( ) ( ) ( )
( ) ( )
( )
F
FBA
N
FBAFN
BpAFN
pDNyMCC
FpFONC
Fy
y
F
yyMCyAC
yyMC
y
F
yyACFyyc
2
2
2
2,
*
**
*
*
*
***
2
−
=
−=
−=
=
=
===
=+=+=