4. Suppose a consumer's utility function for goods 1 and 2 is u( y1, y2) = 4y1 + 10y2. Suppose a firm producing good 1 has the production function f(x) = 9/x-2/3, where x is the amount of some input used by the firm to produce output y1. (a) Derive the consumer's Marshallian demand for goods 1 and 2. (b) Derive the consumer's Hicksian demand for goods 1 and 2. (c) Find the marginal product of input x. (d) Suppose that the cost of input x is w = 9 and that the output price is p = 3. Draw the production function for this firm. Also, draw the isoprofit lines whose vertical intercepts are the points (0,12), (0,8), and (0,4). What is the slope of these isoprofit lines? (e) Suppose that the cost of input a is w = 9 and that the price of output is p = 3. How many units of input x will the firm choose to hire? How many units of output will the firm choose to produce? If there are no other costs, what would the firm's total profit be? (f) Now, suppose that the cost of input x drops to w = 6 and that the output price remains at p = 3. Will the firm choose to increase it's output at the new price? What will the firm's new output level be? How many units of the input will the firm choose to hire now? If there are no other costs, what is the firm's total profit