Socia optimum accordin to any Bergman Samuelson social welfare function is pareto efficient.
Suppse W(u1(x11,x12);u2(x21,x22) is the BS SWF. Goods 1 and 2 are rival. No alturism.
W1=dW/du1>0 st transformation function T(x1,x2)=0
Set up the lagrangean,
get that MRS for individual must equal the transformation function for the economy
Usually because one or more second welfare theorem assumptions are violated.
Monopoly-convexity of production (increased return), perfect competition
Involuntary unemployment-imperfect information, convexity
Externalities- incomplete markets
Why markets fail to generate all possible pareto efficient trades.
1. Inadequate control over commodities by agents. Etc. Common property.
2. costs of organising a transaction might be pohibitively high.
Market failure is only sufficient for policy internvention.
1. but welfare theorem is very strict - ie based on the conditions of scarcity.
2. policy interventions are carried out by government. There can be a government failure.
a. govn has imperfect information
b. they amy n0t be benevolent. Govn. are just economic agents