Exercise 1: Aggregate Supply, Long-Run Equilibrium, and Tax 0 if q=0 Suppose, all firms in a competitive industry have the same cost function c(q): = q2+10q+49 if q> 0 900-20p for p < 45 Aggregate demand for the good is D(p) = 0 for p 45 1. Find the long-run, aggregate supply function, and the competitive equilibrium (p*, Q*) in the long run. How many firms are active in the market (i.e. how many firms produce output q; > 0)? 2. The government introduces a per-unit (specific) tax of $3.50. Hence, the price paid by consumers, PD, is no longer the same as the price received by producers, ps. The two prices differ by the amount of the tax and consumers pay a higher price (including the tax) than producers receive (net of the tax). That is, PD pst holds. What are the new long-run competitive equilibrium price, quantity, and number of firms? What are the resulting (aggregate) consumers' surplus and producers' surplus? 3. Under the assumption that the market was efficient (no market failure), the introduction of a tax, results in an equilibrium quantity that is too low (the marginal social value at Q* exceeds the marginal social cost at Q*, therefore more units should have been traded). This inefficiency is the source of a "deadweight loss". In general, deadweight loss (DWL) is defined as the difference between the maximum total surplus (without the intervention) and the achieved total surplus with the intervention (i.e. the tax in this case). Compute the deadweight loss?