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       

Market failure

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