As the manager of a monopoly, you face potential government regulation. Your inverse demand is P = 45 - 1Q, and your costs are C(Q) = 17Q.

a. Determine the monopoly price and output.

Monopoly price: $

Monopoly output:units

b. Determine the socially efficient price and output.

Socially efficient price: $

Socially efficient output:units

c. What is the maximum amount your firm should be willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimal level?

$

An equity pays half-yearly dividends. A dividend of d per share is due in exactly 3 months' time. Subsequent dividends are expected to grow at a compound rate of g per half year forever. (i) If i denotes the annual effective rate of return on the equity, show that P, the price per share, is given by: d(1+" P =- [3] (1+1)" - (1+g) (ii) The current price of a share is $3.60, dividend growth is expected to be 2% per half year and the next dividend payment in 3 months is expected to be 12p. Calculate the expected annual effective rate of return for an investor who purchases the share. [3] [Total 6]The random variable X has a generalised Pareto distribution with density function. f(x;a) given by: f(ca) = a(a +1)(1,000)" x(1,000 + x)-@-2 A sample of 100 values of X gives the following information: 100 E loge (1,000+ x;) = 750 (i) Calculate the maximum likelihood estimate a of or. [6] (ii) Estimate the standard deviation of a . [3] [Total 9]