Answer Happy

A monopolist produces the good z with costs of c for each unit of r. The inverse demand function is given by p(z)= a-br (with a, b > 0). a) The monopolist has to pay a tax t (with 0 < t < 1) on his profits. What is the monopolist's optimization problem? Calculate the profit maximizing price and quantity from the first-order conditions. b) Now suppose that the monopolist has to pay the tax f not on his profits but on his revenues. What is now the monopolist's optimization problem? Again, calculate the profit maximizing price and quantity from the first- order conditions. c) Suppose the relevant tax regime is the one from question b). How does the monopolist's profit change with a marginal increase in the tax rate t? Calculate the quantitative effect (i.e. the derivative) of an increase in t on profits and indicate the qualitative effect (i.e. whether profit increases or decreases). d) Which theorem can be used in question e) that simplifies the calculation and allows to disregard the indirect effects of a tax increase on the value function (i.e. the optimal profit function)? e) Now suppose that, due to a drop in the supply of input factors, the mo- nopolist can now produce a maximum quantity of = (1- Assume the tax regime from question b). Prove that the restriction is binding for a> E