Caroline owns a business that makes and sells gourmet cookies. Her firm uses a Cobb-Douglas production function given by: F(K, N) = 2KN1-8. She owns 6 commercial ovens that she uses to bake her cookies, so her capital stock is A = 6. Labor (N) is measured as the number of total worker-hours (i.e., the number of hours worked by all of her employees). Each cookie sells at price p = 1. Our job is to determine the optimal labor input to maximize Caroline's profit. 1. Suppose that = = 96, 0 = 1, and the market wage is w = 24 per hour. (a) (1 point) Write down the firm's profit maximization problem formally (mathematically). (b) (1 point) Solve the firm's problem to obtain the optimal labor choice, N. (c) (1 point) How many cookies (total output Y) does Caroline produce? (d) (1 point) How much profit (#) does Caroline earn? 2. Suppose Caroline acquires 2 more ovens, bringing her capital stock up to K = 8. All else remains as in #1 above. (a) (1 point) Solve the firm's problem to obtain the optimal labor choice, N. (b) (1 point) How many cookies (total output Y) does Caroline produce? (c) (1 point) How much profit (#) does Caroline earn? (d) (4 points) Explain why Caroline changed her optimal choice for N* compared to #1. (Hint: recall the optimal condition MPy = w.) How did the change affect the firm's output and profit? What would have been output and profit if the firm had maintained the same N* you found in #1