Assignment Problem: The market for energy drinks is dominated by two major producers: Red Monster and Bull. Knowing that their products are weakly differentiated, the companies have found a way to sustain prices well above their marginal costs through tacit collusion. While the marginal costs equal $3 for a 12-pack for either company, the companies have been charging $18 for a 12-pack in the recent years.
a. Suppose that the price that the two companies chose, $18, is the price that maximizes the industry's profits (i.e., the price that a monopoly company would choose if it had the same cost structure). What does this tell you about elasticity of demand for energy drinks?
Knowing the importance of a healthy energy drink to students and faculty alike, Kellogg graduates of 2023 started a company that would produce a new energy drink from organic ingredients using traditional recipes from world cultures. The marginal cost of the new drink is going to be $6 per 12-pack (which is understandably higher than that of the major competitors, both due to a smaller scale and higher quality ingredients). The new company (and the drink itself) is named Brave Purple (BP). Through market research, you established that demand for the new drink in Evanston is well-described by the following formula:
?????? = 150 -10?????? + 5????????,
where ?????? is Brave Purple's price, ???????? is the price charged by Red Monster and Bull (they charge the same price due to tacit collusion), ?????? is the quantity demanded, in units per day.
Since Red Monster and Bull are national brands and Brave Purple is a small local competitor, you have reason to believe that Brave Purple's pricing decisions will either be unnoticed by the two major companies, or in any case they would not be a sufficient reason to upend the tacit collusion and risk a price war.
b. How would you price the new product? What quantity would you produce and what would be your profit?
The remainder of this question posits different scenarios and asks for your recommendations.
IMPORTANT: Consider each of the following scenarios independently, unless stated otherwise. Explicit calculations are not required (or even possible). However, please clearly explain your reasoning. Use diagrams wherever appropriate.
c. Red Monster airs a negative ad about Bull products, triggering a price war between the two brands. Should you increase the price or decrease the price of Brave Purple? Would you produce less or more? What would happen to your profits?
d. To prevent energy drinks from being used at parties, the city of Evanston attempts to prohibit the sale of energy drinks after hours. Specifically, it bans the sale of drinks that contain taurine after 8pm. Fortunately for you, while Red Monster and Bull contain taurine, Brave Purple does not. Would you recommend adjusting the price of Brave Purple? If so, how? (Hint: the tacit collusion has not broken down!)
e. A trade war with Russia and China begins and pine nuts, an essential ingredient in Brave Purple, increase in price considerably. What would be your recommendation?
f. Brave Purple, consistent with its name, put big letters B and P on the cans. A London-based gas company that uses the same letters as part of their brand sent Brave Purple a cease-and-desist letter. After some negotiation, they reached a settlement that allows Brave Purple to keep using the letters on energy drinks in exchange for a one-time payment of $150,000. How would you recommend that Brave Purple change their pricing policy?
g. Red Monster and Bull merge, and the resulting economies of scale reduce the marginal cost of the merged firms' products by 20%, from $3 to $2.40 per 12-pack. Do you expect them to increase the price, decrease it, or keep it constant? What would you recommend Brave Purple to do? (Hint: Remember $18 was the optimal monopoly price in part a.)
h. Shortly after the merger in part (g), while shopping in a local supermarket, you notice that the price of Red Monster is no longer at the monopoly level as in (g) - in fact, it is exactly equal to the price of Brave Purple. The price of Bull, however, stays the same. After some research, you figure out that this is true in other local supermarkets as well, but not in supermarkets elsewhere in the country where both prices remain at the monopoly level. What would you do? Explain.