Information & Externalities: Cheat Sheet
Based on Varian’s Microeconomics
1. Uncertainty Samuelson Condition
We deal with risky outcomes (x1 , x2 ) with probabilities Efficiency requires summing marginal valuations verti-
(π1 , π2 ). cally.
n
X
Expected Utility (EU) M RSi = M RT
i=1
Rational agents maximize EU, not Expected Value (EV ).
(Sum of willingness to pay = Marginal Cost).
EU = π1 u(x1 ) + π2 u(x2 )
Free Rider Problem
Risk Attitudes Private provision fails because individuals equate M RSi =
M C, ignoring the benefit to others.
Defined by the curvature of u(w).
X
M RSi > M RSi
• √
Risk Averse: u′′ (w) < 0 (Concave). Example:
w, ln(w).
Result: Underprovision.
• Risk Neutral: u (w) = 0 (Linear).
′′
• Risk Loving: u′′ (w) > 0 (Convex). 4. Asymmetric Information
Certainty Equivalent (CE) Adverse Selection (Hidden Info)
The guaranteed amount that gives the same utility as the Example: Used cars, Health Insurance. Bad types drive
lottery. out good types.
u(CE) = EU
• Death Spiral: High price → Good types leave →
Risk Premium: ρ = EV − CE. Average quality drops → Price drops → More good
types leave.
• For Risk Averse: CE < EV (ρ > 0).
Moral Hazard (Hidden Action)
2. Externalities
Example: Insurance leading to recklessness.
When an agent’s action affects another’s utility/cost out-
side the market. • Solution: Align incentives (deductibles, copays).
Social Marginal Cost (SMC) Signaling (Spence)
SM C = P M C + M D Good types take costly actions (education) to prove their
worth.
Where P M C is Private MC and M D is Marginal Damage.
Efficiency: Price should equal SMC, not PMC. • Separating Equilibrium: Cost of signal is lower for
good types, so only they send it.
Solutions
• Pigouvian Tax: Set tax t = M D(y ∗ ). This forces 5. Asset Pricing
the firm to internalize the cost.
Risk-averse investors require higher returns for risk.
• Coase Theorem: If property rights are defined and
transaction costs are zero, bargaining leads to effi-
ciency regardless of who holds the rights. CAPM Formula
• Cap and Trade: Quantity regulation with tradable
permits. ri = rf + βi (rm − rf )
• Only Systemic Risk (β) is rewarded.
3. Public Goods
• Idiosyncratic risk can be diversified away.
Goods that are Non-Rival and Non-Excludable.
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Based on Varian’s Microeconomics
1. Uncertainty Samuelson Condition
We deal with risky outcomes (x1 , x2 ) with probabilities Efficiency requires summing marginal valuations verti-
(π1 , π2 ). cally.
n
X
Expected Utility (EU) M RSi = M RT
i=1
Rational agents maximize EU, not Expected Value (EV ).
(Sum of willingness to pay = Marginal Cost).
EU = π1 u(x1 ) + π2 u(x2 )
Free Rider Problem
Risk Attitudes Private provision fails because individuals equate M RSi =
M C, ignoring the benefit to others.
Defined by the curvature of u(w).
X
M RSi > M RSi
• √
Risk Averse: u′′ (w) < 0 (Concave). Example:
w, ln(w).
Result: Underprovision.
• Risk Neutral: u (w) = 0 (Linear).
′′
• Risk Loving: u′′ (w) > 0 (Convex). 4. Asymmetric Information
Certainty Equivalent (CE) Adverse Selection (Hidden Info)
The guaranteed amount that gives the same utility as the Example: Used cars, Health Insurance. Bad types drive
lottery. out good types.
u(CE) = EU
• Death Spiral: High price → Good types leave →
Risk Premium: ρ = EV − CE. Average quality drops → Price drops → More good
types leave.
• For Risk Averse: CE < EV (ρ > 0).
Moral Hazard (Hidden Action)
2. Externalities
Example: Insurance leading to recklessness.
When an agent’s action affects another’s utility/cost out-
side the market. • Solution: Align incentives (deductibles, copays).
Social Marginal Cost (SMC) Signaling (Spence)
SM C = P M C + M D Good types take costly actions (education) to prove their
worth.
Where P M C is Private MC and M D is Marginal Damage.
Efficiency: Price should equal SMC, not PMC. • Separating Equilibrium: Cost of signal is lower for
good types, so only they send it.
Solutions
• Pigouvian Tax: Set tax t = M D(y ∗ ). This forces 5. Asset Pricing
the firm to internalize the cost.
Risk-averse investors require higher returns for risk.
• Coase Theorem: If property rights are defined and
transaction costs are zero, bargaining leads to effi-
ciency regardless of who holds the rights. CAPM Formula
• Cap and Trade: Quantity regulation with tradable
permits. ri = rf + βi (rm − rf )
• Only Systemic Risk (β) is rewarded.
3. Public Goods
• Idiosyncratic risk can be diversified away.
Goods that are Non-Rival and Non-Excludable.
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