Mathematics and Economics

(Michael S) #1
Egoism

Mathematical Formulation


in anonymous situations, an agent cannot debate prices or influence
what others consume
own consumptionx∈RL+, others’ consumptiony∈RK, prices
p∈RL+, incomew> 0
utilityu(x,y), strictly concave and smooth inx
when is the solutiond(y,p,w) of

maximizeu(x,y) subject to p·x=w
independent ofy?

Definition
We say that agentibehaves as if selfish if her demand function
di

(


p,w,x−i

)


does not depend on others’ consumption plansx−i.
Free download pdf