Cournot competition with N firms (numerical)

Let’s assume now specific values for the following parameters: \(\bar{p}=20, c=2, \beta=0.5\)

1. What does the left graph show? Explain all curves.
2. Why is the equilibrium point at the maximum point of $\pi^n$ and at the intersection of $X^{-i}$ with firm $i$’s BRF?
3. What happens to $X^{-i}$ if you decrease the number of firms, $n$? Use the slider on the graph to check and explain.
4. What does the right graph show? Explain both curves.
5. Which parameters affect the two curves? Use the sliders to change the values of the parameters and check how the graph changes.
6. Assume that there are 8 firms in the market (n=8). Calculate the values for: \(x^N(n), X^N(n), p^N(n), \mu(n), \pi^N(n), \Pi^N(n)\) Remember that you can use the formulas we have already calculated in question 1.
7. Use the interactive figures to verify your answers by choosing the relevant values in the sliders.
8. Assume now that the number of firms in the market becomes 17 (n=17). Can you think how the values of the variables you found in part a. above will change?
9. Use the interactive figures to confirm your thinking and explain.
10. Now, let’s decrease $\bar{p}$ to 11. How do the equilibrium output and markup change? Explain.
11. What happens to the equilibrium price and the markup if $\beta$ decreases to 0.3? Explain with reference to what $\beta$ means and how we think about it in the model.