Assume that a firm has production function of the general form=(,,) and is a price-taker in both the output and input markets such that the price vector it faces (,,,) is given. You may interpret K as man-made capital, Las labor, and N as raw material or natural resources.

(a)Give formal mathematical statements of (i) the firms cost-minimizing problem and (ii) the firms profit-maximizing problem.

(b)Describe the relationship between the cost-minimizing problem and the profit-maximizing problem in terms of any differences and similarities.

(c)Provide an alternative optimization criterion/rule/strategy that a firm might employ to guide its business decisions. Describe the associated optimization mathematically and graphically. [Be careful to declare the meaning of any symbols (variables and/or parameters) that you introduce in your analysis and label all graphical objects.]

(d)For the profit-maximizing problem, provide a generalized solution function for N. Characterize the expected properties of this solution function mathematically, graphically, and, concisely, verbally.