06.11.2023 Externalities#

Externalities: situation, where ones party action affects others, but is not compensated

Example: Pollution, Education

Externalities = market failure => government intervention

Externality Theory#

Types:

  • positive / negative (Pollution / Education)

  • from production / from consumption (Pollution / Smoking)

Example: Steel Company

  • Production of steel and sludge

  • 1 unit of sludge for every unit of steel

  • sludge directed into stream, kills fish from fishers

Externalities: SMC \(\neq\) PMC

Private Marginal Cost (PMC): direct cost to produce one good

Social Marginal Cost (SMC): PMC + costs imposed on others

Example: img

Types of Externalities:

  • negative production: SMC > PMC

  • negative consumption: SMB < PMB (Private Marginal Benefit)

  • …

Solution: internalize Externalities

  • private negotiation

  • government solutions

Private Sector#

Coase Theorem: well defined property rights + negotiations => socially optimal market quantity

Example:

  • Fishers own the property rights

  • negotiate compensation with steel plant

img

Important: Efficient solution does not depend who owns the property rights!

Problems: (especially with many people)

  • Assignment Problem

    • who causes the damage?

    • how large is the damage?

  • Holdout Problem

    • shared ownership of rights = veto options

    • may demand enormous payments

  • Free Rider Problem

  • Transaction Costs / Negotiationg Problems

=> Coase only works with specific problems!

Public Interventions#

Instruments:

  • Taxation / Subsidies

    • internalize externality

    • correct tax = Pigou Tax

  • Regulation

    • regulate Quantities

    • complicated information needed

Price-Based Approach vs Quantity Based Approach

Distinction#

Right Amount of Pollution

img

  • A = free market

  • B = socially optimal: SMC = SMB

Example 1: Multiple Plants with differenct reduction costs

img

  • blue line = Tax (efficient)

  • black line = Regulation

Example 2: unvertainty about costs

  • high SMB of Reduction => Quantity Based Approach (nuclear leakage)

  • Low SMB of Reduction => Price Based Approach (kg of carbon)

High SMB:img

Assumption of MC1

  • C = Regulation and Tax

if real MC = MC2

  • E = Tax

  • A = Regulation

  • DWL Regulation < DWL Tax

=> when Quantity is important use Regulation, else taxes

Tutorial: Addition of Demands#

  • Vertical Summation = Add up at Quantity Q (Public Good)

  • Horizontal Summation = Add up Demands at Price P

Example Horizontal:

  • A: \(Q = 21-6P\)

  • B: \(Q = 6-3P\)

Addition of the Quantites at given Price $\( Q_1 + Q_2 = (21-6P) + (6-3P) = 27-9P \\ 9P = 27 \to P = 3 - \frac{ 1 }{9}Q \)$

Example Vertical

Solve indivudally for P (Demands from above)

  • A: \(P = \frac{ 7 }{2} - \frac{ 1 }{6}Q\)

  • B: \(P = 2 - \frac{ 1 }{3}Q\)

Sum up

\[ P_1 +P_2 = (7/2 - 1/6Q)+ (2 - 1/3Q) = \frac{ 11 }{2}- \frac{ 1 }{2} Q \]

Bike Paths Example#

individual Bike Path Demand

  • A: \(Q=24-4P\)

  • B: \(Q = 14-P\)

  • C: \(Q = 5-1/3P\)

Marginal Cost of one Path = 18

Version 1

  • town decides to tax evenly

  • asks residents, highest number answered gets build

  • \(MC = a+b+c\), here (a=b=c)

  • 18/3 = 6 Cost Units

Demands at this Price (input P=6)

  • A: Q=0

  • B: Q=8

  • C: Q=3

=> Build 8 Paths

Version 2: Social Optimum

  • solve every Demand for P

  • sum Up => SMB

  • SMB = MC = 18, solve for Q

  • insert Q into individual Demand Functions