2.Properties of PS.
• Additive (free entrance) :
y Y,and y Y, then y y Y • Convexity: y Y,and y Y, then y (1 )y Y, here [0,1]
See the fig.
• Proposition1: if Y is convex, so is V(q). • Proposition2: if V(q) is convex, f(x) is quasiconcave.
lecture 1 for Chu Kechen Honors College
y Y, ay Y, a 0
lecture 1 for Chu Kechen Honors College
4.Returns to scale
• Proposition 3: Y is constant returns to
scale if Y is both “additive” and “convexity”. • Proposition 4: single production, if and only if f(.) is homogenous of degree 1, Y is constant returns to scale.
the array y y, and y Y means y Y • No free lunch: Y n {0}
n n
See the fig.
• Free disposal:
See the fig.
lecture 1
y n Y
for Chu Kechen Honors College
