Question

Imagine that you are an economist working with Augustin Cournot during the 1840’s. You have decided to diversify and start a business selling Cockroach Cluster candy bars. Unfortunately for you, Mr. Cournot gets wind of your idea and decides that he would like to start his own business in order to capture some of the Cockroach revenue for himself. Now you find yourself in a simple game of price competition. Assume that each of you has a fixed cost of $500, which must be paid regardless of how many candy bars you sell. The two of you must compete in price given that you can charge a price of either $3, $2, or $1. At a price of $3, 250 candy bars are sold for a total revenue of $750 dollars. At a price of $2, 500 bars are sold for a total revenue of $1000. At a price of $1, 1000 bars will be sold for a total revenue of $1000. Total revenue is calculated by multiplying the price at which the product sold times the total quantity that was sold at that price. Now, if both of you charge the same price, then you will split the sales evenly between the two of you. But, if one of you undercuts the other, then the person with the cheapest price captures all of the sales in the market. Depending on the chosen price and the information provided above, firms earn profits, which can be derived by subtracting the fixed cost from the total revenue. For simplicity, let us assume that Mr. Cournot has named his company The Rizzo Chocolate Factory (TRCF) and you have chosen to name your company The Spring Surprise Candy Company (SSCC).
a. Set up the game using the normal / strategic form.
b. Are there any strictly -dominated strategies? If so, is there an I.E.S.D.S. equilibrium?

Answer 1

a) We have three strategies that each of the players will face, low price ($1), medium price ($2) and high price ($3). Suppose that SSCC charges a price of $2. Now if TRCF charges a price of $1, it gets all the consumers and sells 1000 bars at a price of $1. Revenue is $1000 and cost is $500. This implies TRCF makes a profit of $500 while SSCC bears a loss of fixed cost which is $500. Similarly the payoffs are computed for other combinations.

b) Using  I.E.S.D.S, we eliminate a high price strategy for both firms because it is never chosen. After deleting them we get a 2 x 2 matrix that has a unique equilibrium where both sells at a price of $1 and earn no profit.