Mathematics for Economists

Dynamic programming

The main advantage of the compact valued and continuous

correspondences is that the parametric optimization problem

g(s)$maxfU(s,x)jx 2 Φ(s)g

is a continuous function of the parametersassuming thatUandΦare

continuous andΦis compact valued. In this case the correspondence

Ψ(s)$fxjx 2 Φ(s),U(s,x)=g(s)g

is upper semi continuous.