Summer of Math Exposition

This is a solution to the Duoploy Problem using Desmos. The Duoploy problem is a famous problem in economics and game theory in which there are two firms competing against each other in order to maximize their profit. Each firm has to make the decision of how many items they should produce. But the optimal number of items that a company should produce does not simply depend on one firm. The optimal number of items that one firm produces is inherently dependent on the number of items the opposing firm produces. The more items produced decreases the price since the price is inversely proportional to the number of items produced. If the price goes too low, then the profit would also decrease even though more items are being sold because the cost of production would cancel out the revenue generated. So each firm should consider what strategy the opposing firm is using in order to maximize the profit. The optimal strategy is found by finding the point where both firms would be doing worse off if they were to slightly deviate from that point. This special point is called the Cournot Nash Equilibrium. In this project, you can input any function you want for the profit and the average cost of production to calculate the Cournot Nash Equilbirum.