Let's pretend the market for Soda is for all intents and purposes a monopoly in our fictional country the Republic of Stark. Stark soda has an overwhelming market share. The demand for Stark Soda for each year is given by: = 500 - 10P.

Stark Soda has a single plant (hidden below the classroom) that it built for $10 million dollars. Each year it has a loan repayment of 6 million to pay off the loan it took out to finance the plant. The plant itself is fairly specialized and has zero scrap value, but it has some equipment that is worth 10 million if the plant is closed and sold off. If they decide to produce, Stern Soda enters into a bulk electricity and water contracts at the start of each year for which they pay 2 million upfront for all the electricity and water they want. The firm's marginal cost, which is mostly labor, maintenance and ingredients (Flavoring, Carbonated Water and Sweeteners), is $2 per unit.

(a.) Before the beginning of each production year, what parts of the firm's fixed costs are sunk?

(b.) How does your answer to (a) change if we are in the middle of a production year?

(c.) Draw a graph of the marginal cost curve.

(d.) Derive the marginal revenue function for Stark Soda.

(e.) Draw a diagram with Price on the vertical axis and Quantity on the horizontal axis that shows the Demand curve, Marginal Revenue curve and Marginal Cost curve.

(f.) Derive the optimal price and quantity for Stark Soda given the following:

Revenue = (50 - Q/10)*Q-8000000-2Q d/dQ((50 - Q/10)*Q-8000000-2Q) =-1/5Q+48 48=1/5 Q=240