Question: A firms technology is defined by the production function: Q = 9K^2/3L^1/3

It pays wages @ $18/hour (w) and rents capital @ $36/hour (r).

The demand for its goods is given by the demand function: Q = 240 – 10P

a) What is the firm’s marginal rate of technical substitution (MRTSKL), optimal condition in the product market, optimal inputs in terms of its optimal output, cost constraint in terms of its optimal output (TC), and marginal cost function (MC)? What is its demand function in terms of Q, its total revenue (TR) and marginal revenue (MR) functions?

b) What is the firm’s profit-maximizing levels of price (P*), output (Q*), capital (K*), labor (L*), and profit (?*)?

c) What is the firm’s revenue-maximizing levels of price (P), output (Q), and profit (?)? Which of (b) or (c) is better?