Question: Suppose there are 4 identical firms in the market. The total cost of each firm is given by \(T C(q)=\) \(50+q+2 q^{2}\). The demand for the product is given by \(Q_{D}(p)=81-p\). Suppose also that all fixed costs are sunk in the short run.

1. find the firm's supply curve, \(q(p)\)
2. find the market short-run supply curve, \(Q_{S}^{S R}(p)\)
3. find the short-run equilibrium price, \(p_{0}\), equilibrium individual output, \(q_{0}\), and equilibrium total output \(Q_{0}\)
4. does a typical firm earn any profit in the short-run equilibrium?
5. find the market long-run supply curve, \(Q_{S}^{L R}(p)\)
6. find the long-run equilibrium price, \(p^{*}\), equilibrium individual output, \(q^{*}\), equilibrium total output, \(Q^{*}\), and equilibrium number of firms, \(n^{*}\)
7. does a typical firm earn any profit in the long-run equilibrium?

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