1. A company in a competitive market with a cost function C(q) = 100 + 10q - q2 +13q3has learned that it will now have to face a specific tax of τ = $10 (per unit). This specific taxmeans that for every unit of output the firm sells it has to pay a tax of τ dollars. If the firm sells qunits, it pays a total tax of qτ.
(a) What is the firm's cost function including the tax?
(b) What is this firm's short-run profit-maximizing output if the market price is p? (Hint: the solution has to be expressed as a function of p and has to be defined for valuesthat make economic sense, e.g. only positive quantities.)
2. A monopolist faces the inverse demand for its output: p = 30 - Q. The monopolistalso has a constant marginal and average cost of $4/unit.1
(a) What is the monopolist's profit-maximizing level of output? What is the monopolist'sprofit at this level of output?
(b) What is the consumer surplus? Show it in a graph along with the monopolist'sequilibrium; label the monopolist's equilibrium eM.
(c) What would the competitive equilibrium be if the demand curve were the same asthe one faced by the monopolist and the market supply curve were equal to the monopolist'smarginal cost, i.e. P = MC? Show this equilibrium in the same graph as above and label iteC.
(d) What is the gain in consumer surplus if this market were perfectly competitiveinstead of a monopoly?