Class notes
Lecture notes on Public Goods and Externalities
- Course
- Institution
Lecture notes on Public Goods and Externalities with notes on supplementary readings
[Show more]
Seller
Follow
ollieasjones
Content preview
Add in-depth VCG notesPublic Goods and Externalities
Measuring Welfare
CS: difference between WTP and amount paid
EV: income required at old prices to maintain new utility
CV: income required at new prices to maintain old utility
Quasilinear Preferences
Demand for nonlinear good independent of m – no income
effect except for low incomes – indifference curve vertical shift
EV=CV=∆CS – aggregate indirect utility = sum of indirect utilities
k 1 ∂C k
M comes from fact consumer owns firm: m=π =Σ pk y −C ( y , … y ) ⇒ = pk
∂y
1 k
u=u ( x , … x )+ π −Σ k p k ⇒ in eqbm consumption = production and m=π
u=u ( x1 , … , x k ) −C ( x 1 , … , x k ) ie benefit – cost so MB= p=MC ie P-efficient
Effect of Tax (not lump sum)
Wedge between consumer and producer price prevents profitable
trades so DWL
Raises revenue for government
Δ p< 0 , Δ x< 0
Δp p
u' ( x ) =p ⇒ u'' ( x )== <0 recall ε D = Δ x p >0
Δ x x εD Δp x
ΔC C
' ''
C ( x )= p ⇒C ( x )= = > 0 recall ε s= Δ x p > 0
Δ x xεs Δp x
'' −pΔx '' p Δx
Δ p+ τ= Δ x u ( x )= ; Δ p=Δ x C ( x )=
x εD x εs
Δ xτ −1 τ 2 εD εs
DWL=
2
=
2 p
px () (
ε s−ε D )
=tax ⋅ sales ⋅ constant
Increasing in: square of tax, sales, elasticities
Burden depends on who has relatively more inelastic curve
Optimal Commodity Taxation
k
Raise revenue, min DWL: min Σ k DW Lk s . t . Σ k τ k x ≥ G
τi/ pi ε j
Assume: linear D, constant MC, XED=0, no lump sum tax ⇒ = ⇒ tax inelastic
τ j / p j εi
goods more, but all goods in proportion to required revenue. Optimal taxes regressive
Monopolist Inefficiency
−1
Constant MC⇒ ε s=∞, mark up of μ ⇒ DWL= μΔx
2
¿ x
p ( 1+ε D )
¿ ∗¿
¿∗¿
¿ −1 p −1 ¿∗¿ ε ¿
¿∗¿= p + μ= ⇒ DWL= Δ x= p ¿¿ ¿
εD 2 εD 2
p
As ε D evaluated at p¿∗¿, x
¿∗¿¿
¿
Cost-Benefit Analysis
Σ ( Bt −Ct )
NPV =
( 1+r )t
Can't value at market prices as gen eq effects, non-marginal changes of p and q, market
failure / shadow prices, non-market valuations
General Equilibrium Effects
Project will directly affect some quantities (inputs), and indirectly affect all others
U =u ( x1 , … , x k ) −Σ p k x k + Σ p k y k −C ( y 1 ,… , y k )
, Add in-depth VCG notes
k k k k
dU ∂u d x dx dy ∂C d y
=Σ k −Σ +Σ −Σ k
d pk ∂x d p k d p k d pk ∂ y d pk
∂u ∂C
dU =Σ ( y k −x k ) d p k + Σ
k k
∂x
k(− pk d x k −Σ
∂y )k (
− pk d y k = Δ p + Δ q
)
Price change: if y =x just a transfer, no ∆W – do not value unless i) social value of income
different for gainers / losers (depends on W ( u ) ) ii) if y k ≠ x k then terms of trade effect: gain if
price increase on exported good (Stolper-Samuelson)
Quantity change: if perfect economy ie u' = p=c ' then no social value – ignore gen eq
effect in other markets; if imperfect, positive social value to expanding for u' >c ' , positive
value to contracting if u' <c ' - need to know valuations and quantity changes
Market Failure and Shadow Prices
Monopoly: p> MC ⇒ MC is resource cost, p−MC is transfer to monopolist, not real RC
Unemployed labour: if unemployed people, shadow price is op. cost of employing worker; if
otherwise employed, shadow price = wage = VMPL in other job; if unemployed, w=0? Or
value of leisure foregone?
General principle: identify opportunity cost
Non-Marginal Changes
Project increases output by non-marginal amount x ' → x' ' ⇒ p' → p' '
'' '' ' ( p' − p' ' ) ( x ' ' −x ' )
B = social value of extra output: p ( x −x ) + ie Δ TR+ Δ CS
2
Commercial decisions do not account for ∆CS – very small for marginal changes
Social Discount Rate
' '
Value of marginal consumption today ¿ u ( xt ) e ⇒−log u ( x t ) + ρt [ ]
−ρt
' '' ''
d −1 ∂ u ( x t ) dx −u ( x t ) dx −u ( x t ) dx 1
= ' + ρ= ' + ρ= ' xt ⋅ +ρ
dt u ( xt ) ∂ x dt Time u (Rate dtMU of
x t )at which uElasticity
( x t ) of dt Consumption
xt
preference consumption falls MU of growth rate
consumption
Social Discount Rate
''
−u ( xt ) dx 1
r= '
xt ⋅ +ρ
u ( xt ) dt x t
''
−u ( x t )
'
xt : determines how fast MU falls: prefer equality over space and time
u ( xt )
dx 1
: less weight on future generations if they are much richer: C growing fast
dt x t
ρ : impatience, extinction probability, generational bias
Externalities
Action of an agent directly affects utility of another. Pecuniary externalities relate to prices
and do matter with frictions, but don’t exist under perfect competition
Taxonomy:
Rival Non-Rival
Excludable Private Good Club Good
Non-Excludable Commons Good Public Good
Consider: scale, scope, time, distribution, reversibility
Pure Public Goods Model
x , y are public and private goods, u=v i ( x ) + y i s .t . M i ≥ x + y i
MRS=v 'i ( x )=M Bi ( x )=1
Under-provision
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ollieasjones. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.95. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
85443 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now