Problem
You own a brussel sprout juice bar in Georgetown. The daily demand that your brussel sprout juice bar faces is: Q(P) =100-P . The total daily cost of operating the juice bar is:
TC(Q) =100+10Q
I. What is your juice bar's marginal revenue function? You are interested in maximizing revenue. How much will you produce? What price will you charge? How much will your daily profit be?
II. You are now interested in maximizing profit. How much will you produce? What price will you charge? How much will your daily profit be?
III. Compare the profit that you calculated in part a. to the profit in part b. Does it make more economic sense to maximize profit or maximize revenue? Explain.
IV. You have brought in a market consultant with a UMD degree who explains to you that that the demand you face is not what you thought. He says that the juice bar's demand function is actually Q(P) =50-P . If this is so, how much will you produce? What will you charge? How much will your daily profit be?
V. You decide that the UMD graduate is wrong and your juice bar's demand function the original Q(P) =100-P . You bring in a narcissistic NYU graduate who explains your total daily cost function for the juice bar is TC(Q) =50+8Q. If this is so, how much will you produce? What will you charge? How much will your daily profit be?
VI. Finally, you bring in a low-key (but impressive) Georgetown graduate. Based on her expansive and balanced knowledge of economics (she knows about demand as well as costs), she explains to you that your cost function is actually TC(Q) =100+Q2 and the demand function you face is actually Q(P) = 20-P . If this is so, how much will you produce? What will you charge? How much will your daily profit be?