3. Competive budget >Consumption set X and it's price pcR with the wealth w>0 >Definition: Walras(competive) budget set B(p,)={x∈9:p·X≤w} >Proposition: if X is concave, then is B(p, w) lectures for Chu Kechen Honors College
lecture5 for Chu Kechen Honors College 3.Competive budget ➢ Consumption set X and it’s price with the wealth w>0. ➢ Definition: Walras (competive) budget set ➢ Proposition4: if X is concave, then is n p ( , ) { : } n B w w p x p x = + B w ( , ) p
4 Demand function For any p and w are strictly positive, the corresponding demand set x(p, w)are nonempty, if x(p, w) is single point, we call it the Walrasian( marshallian) demand function > x(p, w)is homogenous of degree zero and satisfied Walras'law. That is pxw for all X∈X(p,w)andp>0,w>0 (we will prove them next lecture) lectures for Chu Kechen Honors College
lecture5 for Chu Kechen Honors College 4.Demand function ➢ For any p and w are strictly positive, the corresponding demand set x(p,w) are nonempty, if x(p,w) is single point, we call it the Walrasian( Marshallian) demand function. ➢ x(p,w) is homogenous of degree zero and satisfied Walras’ law. That is px=w for all (we will prove them next lecture) x x p ( , ) and 0, 0 w p w