2. Scoops Ahoy is an ice cream shop in Starcourt Mall. Scoops makes ice cream cakes using capital, K, and labor, L, according to a production function q = KALA. The price of capital is r, and the price of labor is w. The shop is under new management, and the owner is making a plan about the profit maximizing number of ice cream cakes to produce. a. The owner's friend, Dustin, says that the first step is to figure out costs of producing a given q. In the short-run, the amount of capital Scoops has is fixed, at value K, and so there is a fixed component of short-run costs. Write down a formula for short-run costs for Scoops. b. Now write down the short-run profit function for Scoops. c. Take the derivative of the profit function and set it equal to zero. Move all terms that do not involve Pc to the right hand side. Interpret both sides of the equation, using the concepts of marginal revenue and marginal cost. d. Now solve the equation you found in the previous part for the profit maximizing q. How does this formula relate to the short-run market supply curve of ice cream cakes?