1. For the following cost functions

(a) c(w,q) = q(w1 +w2);
(b) c(w,q) = q(w1∧1/3× w 2∧1/3);
(c) c(w,q) = q×根号下w1的平方加上w2的平方

i). find out which one(s) cannot be a cost function? Justify your answer.
ii). if it is a cost function, please use Shephard’s Lemma to derive a production function for
which c is the cost function.

2 2
Let f,v : R+ → R+. Define the function c : R+ ×R+ → R+ by
c(w1,w2,q) = f(w1)+v(w2)q
(a) What properties must f and v satisfy for c to be a cost function?
(b) Can you find a technology for which c is the cost function?
(c) Give an economic interpretation of f and v.

3 Let 弱偏好序be a regular preference relation on a set X.

Prove that 严格偏好序 and ～ are transitive.