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

qq

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