Consider a market with 9,000 identical consumers. Each consumer utility function is given by U(q, m) = 2*sqrt(q) + m, where q denotes the amount of widgets that she consumes, and m denotes the amount of $ consumed. The market is supplied by 20 identical competitive firms, each with a cost function given by c(q) = q^2.

Suppose that the government introduces a 10% revenue tax on sellers (i.e, firms pay 10% of their sales revenues as taxes, and keep the other 90%), and that it returns the revenue to consumers using an identical lump-sum transfer.

(The answers need to be precise up to 2 decimal points).

What is the equilibrium price in this market? Suppose that the goverment considers an alternative policy involving no tax on firms, but a 10% ad-valorem tax on consumers (so that a $1 dollar purchase costs $1.10 after taxes).

What is the equilibrium price in this case?

What is the total level of widgets produced at the Pareto optimal allocation?