Ecological EconomicsWeek 4
Tiago DomingosAssistant Professor
Environment and Energy SectionDepartment of Mechanical Engineering
Doctoral Program and Advanced Degree in Sustainable Energy Systems
Doctoral Program in Mechanical Engineering
• Choice
2
1
22
122
2
..
2max
C
L
C
L
C
L
cL
cL
p
p
p
mC
p
p
p
mL
mCpLpCLLC
mCpLpts
CLLCU
Assignments
L
C
p
mLthenCIf
p
mCthenLIf
CandL
0
0
00
Normal goodsOrdinary goodsSubstitutes
• Profit maximization
Assignments
15.01200
15.00
400300
2
p
pfor
N
NNNY
• Cost minimization– We want to solve the following problem
– The production isoquants show that the solution must be a corner solution
yxxts
xwxwmín
2
1
221
2211
2..
Assignments
x2
x1
• Cost minimization– But if you did not noticed then and solved the lagrangian:
– Corner solutions:
Assignments
22112
12
22
21
220
20
ywy
wify
xx
ywywifyxx
This is not a possible solution since they are both Giffen goods and it is not possible to have a fixed cost unless it is explicit in the problem. It must have a corner solution2
2
212
2
2
11
8
4
w
wyx
w
wx
Cost curves (1/3)
• Family of cost curves
• Marginal cost (MC)
– change in cost due to change in output
AFCAVCAC
y
F
y
yC
y
yC
FyCyC
v
v
dy
ydC
dy
ydCyMC v
Cost curves (2/3)• Marginal cost
– marginal cost equals AVC at zero units of output– goes through minimum point of AC and AVC
– this is negative (for example) when c′(y) < c(y)/y– fundamental theorem of calculus implies that
dy
ydC
dy
ydCMC v
dttCyCy
v 0
Cost curves (3/3)
• Marginal cost– geometrically: the area under the marginal cost curve gives
the total variable costs. Figure 20.3.
– intuitively: the marginal cost curve measures the cost of each additional unit, so adding up the marginal costs of each unit gives the variable cost
Firm supply
• Supply curves of a competitive firm– A competitive firm ignores its influence on the market price.
– Two conditions:
– Long run:
– Short run:
– The I represents the point where
0
max
***
yCpy
yCpyy
0
0
p p
AC
y
yCp
AVC
y
yCp v
Industry supply
• Industry supply curve– Let be the supply curve of firm i, so that the industry
supply curve, or the market supply curve is:
pSi
n
i
pSipS1
p
y
S1+S2
S1
S2
• Demand versus Supply curve– If we let be the market demand curve and the
market supply curve, the equilibrium price is the price that solves the equation
Q
MPC = supply curve
MPB = demand curve
Market equilibrium
pD pS*p
** pSpD
q*
p*
q
p
• Consumer surplus
Q
MPC = supply curve
MPB = demand curve
Market equilibrium
q*
p*
*
0
q
dqpMPB
q
p
• Producer surplus
Q
MPC = supply curve
MPB = demand curve
Market equilibrium
q*
p*
*
0
q
dqMPCp
p
q
• Social balance– Consumer surplus + producer surplus
Q
MPC = supply curve
MPB = demand curve
Market equilibrium
q*
p*
p
q