Question

prove that cost function is a concave function of a input price vector

Answer 1

Answer:

To demonstrate concavity let (w, x) and (w', x') be two cost-minimizing price-factor combinations and let w”= tw + (1-t)w' for any 0 ≤ t ≤ 1. Concavity implies that C(w” y) ≥ tC(w, y) + (1-t) C(w', y). ... Along the cost function, as the price of input i increases, we probably use less of input xi and more of other inputs.