Applied Welfare, Externalities, And Public Goods Flashcards
What is normative individualism?
Normative statements about society based on statements about individual welfare.
How can we measure the effect of a price change from p0 to p1 on the consumerβs welfare if the consumer has fixed income.
If we know the utility function we can compute changes in indirect utility (to obtain indirect utility put the demand functions into the utility function):
u(x(p1, m)) - u(x(p0, m)) = v (p1, m) - v(p0, m)
What is a money-metric measure of welfare?
constructed using the expenditure function
minπ π β π subject to π’ π β₯ π’^-
βΉ π π, π’^- = π β πβ = π
What is the compensating variation
The Compensating Variation (CV) is the amount of money that must be taken from the consumer, given that a price change happens, to ensure they reach the old utility:
π (New Prices, π β πΆπ)= π (Old Prices, m)
What is the equivalent variation
The Equivalent Variation (EV) is the change in income at the old prices that would give the same utility as with the new prices:
π New Prices, π = π(Old Prices,π + πΈπ)
What is the deadweight loss in a quasi-linear model
DWL = (x*-xt) - t / 2
What is the net present value (NPV)
the stream of net benefits discounted for the future
NPV = β(Bt-Ct)/((1+r)^t)
If NPV>0 the project should be undertaken
What is the equation for social discount rate r (Ramsey formula)
π = π + ππ
π is pure rate of time preference
π is elasticity of marginal utility of consumption
π is rate of consumption growth
What is an externality?
An externality is present when an action of one agent directly affects the utility or production possibilities of other agents.
Different types of goods
Private goods: excludable and rival
Commons goods: non-excludable and rival
Club goods: excludable and non-rival
Public goods: nonexcludable and non-rival
What happens when there is a public good which different agents can pay for?
Only the consumer with largest marginal benefit pays!
In game-theoretic terms the Nash equilibrium is {0, π₯π΅
β }
Pareto-efficient provision π₯β is where total demand = supply, so there is underprovision in equilibrium
What is the Samuelson rule?
The sum of the marginal utilities should equal marginal cost
What is Lindahl pricing?
Each consumer reports their
marginal utility function, π’π
β²(π₯). Assume truth-telling
The government adds the marginal utilities, choosing π₯β (with βπ π’β² (π₯β) = π) and sets the unit tax for π equal to their marginal utility at the optimum: π‘π = π’πβ²(π₯β)
By construction total tax revenue equals the cost of the public good: π‘π΄ + π‘π΅ = π’π΄β²(π₯β) + π’π΅β²(π₯β) = π
Lindahl taxation requires that
agents tell the truth about
marginal utilities
How can people be incentivized to tell the truth?
Clarke-Groves mechanism:
The government considers providing a public good. Three agents: 1, 2, 3
* If the good is not provided each net value is 0
* Net values (= gross value minus share of cost) if the good is provided are
π£1, π£2, π£3.
* Each agent reports their net value for the good: π1, π2, π3
* The good is provided if βπ=1
3 ππ > 0, is not provided if this sum is negative, and a coin is tossed if the sum is zero.
- If the good is provided, each agent receives a payment equal to the sum of the reported net values of the other agents: ππ = βπβ π ππ
- If the good is not provided each payment is zero.
- With truth-telling each personβs utility, with the payment, equals total welfare: π£1+ π£2+π£3 if provided, 0 if not
- If the good is provided the government must pay out
2(π£1+ π£2+π£3) > 0
Lying canβt raise agents utility, and could reduce it
What is the Clarke tax?
Clarke proposed an additional tax of π‘π = max {βπβ π ππ , 0}
An agent pays money to the government if and only if they are pivotal. The tax net of the payment is π‘π β ππ β₯ 0
If ππ + βπβ π ππ > 0 and βπβ π ππ < 0, π‘π β ππ = βππ = β βπβ π ππ > 0
If ππ + βπβ π ππ < 0 and βπβ π ππ > 0, π‘π β ππ = π‘π = βπβ π ππ > 0
If π is pivotal then π‘π β ππ equals their effect on all othersβ welfare
