Question: Consider the following duopoly game: each of 2 firms can produce as much of a good as he wishes at marginal cost 1 (i.e., producing \(q\) units costs \(1 \cdot q=q\) in total), and the market demand curve is given by \(X(p)=10-p\).

1. Calculate the price elasticity of demand
2. Find the inverse market demand curve, specifying the price at which \(X\) units can be sold.
3. Write out each firm's profit expression, if firm 1 produces quantity \(x_{1}\) and firm 2 produces quantity \(x_{2}\).
4. We found in class that the NE of this game is for each firm to produce 3 units. If you did (c) correctly, you will see that this yields a profit of 9 to each firm. However, if firms could agree at the start to each produce only 2 units, they would both earn a higher profit, namely 10. Explain why such an agreement might not work.

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