Provide well explained answers to the following questions. Ensure that all questions are addressed as required.

Q1. 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?

$

(i) By considering a term assurance policy as a series of one-year deferred term assurance policies, show that: A [5] (ii) Calculate the expected present value and variance of the present value of a term assurance of 1 payable immediately on death for a life aged 40 exact, if death occurs within 30 years. Basis: 4% per annum interest, AM92 mortality, no expenses. [6] [Total 1 1]A population with limiting age 100 has the following survival function: I Po = 1- for OS/ $ 100 100 Calculate the complete expectation of life at age 50. [3]A student who regularly goes tenpin bowling thinks that he scores higher with one particular bowling ball than he does with his other two. For the next 15 games that he bowls, he chooses a ball at random and notes down the scores as follows: Ball Score sum of squares 173, 166, 179, 183, 199 900 162,616 195, 206, 188, 195, 210, 221 1,215 246,771 3 169, 155, 172, 188 684 117,514 From the data obtained, calculate unbiased estimates of: (i) the overall mean, u (ii) the "treatment effect" for each ball. r