Public Goods & Market Failure

Market Parameters

Number of Consumers (N) 5

Max WTP per person (a) 20

Demand slope (b) 2.0

Marginal Cost (c) 5

Individual: P = a − b·Q
Social: P = N·a − N·b·Q
MC = c (constant)

Policy Instrument

No Policy

Subsidy

Public Provision

Free-rider problem: Each person only considers their own marginal benefit, ignoring others' benefits. The market underprovides.

Subsidy per unit (s) 0

                    Per-unit subsidy: Reduces effective MC faced by the market to MC − s. Set s to close the gap between private and social value.
                

Government Quantity (G) 0

                    Direct provision: Government provides quantity G, funded by taxes. Set G to the socially optimal level.
                

Key Insight

For public goods, the social demand is the vertical sum of individual demands (unlike private goods which sum horizontally). This means the social marginal benefit at any quantity is the sum of every person's marginal benefit.

Public Goods: Market Failure & Policy Correction