复旦大学：《高级微观经济学—均衡理论》英文版 Problem set 2 Prof gene Chang

Problem set 2 Prof gene Chang (For Ph D students, due on Dec. 9th in the class, or TAs office. For M.A. students, due on Dec. 12th, in the class or TA's office. Late turn-in may result in a penalty in the grade) 1. The production set is Y=(yy2):y2≤,-∞≤y1≤l} a) If the price vector is p=((P, p,): P,=l,P2=4), what is its production plan(the netput quantities)of the firm, if it maximizes profits? b)If the price vector is p=((P, P2): P,=5, P2=1/, what is its production plan, if it maximizes c)Plot the corresponding netput supply curve for the firm in the following diagram. Label the numerical value for the intercept of the supply curve P2/P1 2. The increasing returns to scale of the technology is defined as f(rx)=rf(x) k>l, Vi>0 If a technology is increasing returns to scale, formally prove that the convexity of the production set would not hold

Problem Set 2 Prof. Gene Chang (For Ph.D students, due on Dec. 9th in the class, or TA’s office. For M.A. students, due on Dec. 12th, in the class or TA’s office. Late turn-in may result in a penalty in the grade) 1. The production set is 1 1, 2 2 1 1 {( ) : , 1} 1 y Y y y y y y =  −   − . a) If the price vector is 1 2 1 2 p = = = {( , ) : 1, 4} p p p p , what is its production plan (the netput quantities) of the firm, if it maximizes profits? b) If the price vector is 1 2 1 2 p = = = {( , ) : 5, 1} p p p p , what is its production plan, if it maximizes profits? c) Plot the corresponding netput supply curve for the firm in the following diagram. Label the numerical value for the intercept of the supply curve. 2. The increasing returns to scale of the technology is defined as ( ) ( ) 1, 0 k f t t f k t x x =    . If a technology is increasing returns to scale, formally prove that the convexity of the production set would not hold. 0 P2/P1 Y2