Consider a firm with 1 input and 1 output, and a production function given by f (x) = 3x^ with < 1. The cost of the input is c and the price of the output is p.

(a) Write down the profit function and the first order conditions associated with profit maximization. Find the factor demand, x*(p,c).

(b) Verify directly that x*(p,c) is homogeneous of degree 0.

(c) When the price of the output, p, increases, does the demand for the input, x increase or decrease?