Suppose a firm produces a single product y with technology that can be represented by a differentiable, increasing and strictly quasi-concave production function y = f(x)

where

X Rⁿ ₊ is the vector of inputs.

The price of these inputs is given by the price vector

w Rⁿ ₊₊.

(a) State the firm's cost minimization problem

(b) Show that the Lagrange Multiplier from the cost minimization problem equals the

firm's marginal cost.

(c) Show that if f(x) is also a homothetic function then the cost function can be written as

c(w, y) = h(y)c(w, 1)