Address all the questions appropriately. Please no copy pasting from other sources.

1.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?

$

Consider the following Health, Sickness, Death model with the addition of an extra "Terminally ill" state, T. The rates given are per year. 0.02 0.15 H T S healthy terminally sick ill 1.00 0.05 0.05 0.40 D dead (i) Calculate the expected holding time in state S. (ii) Calculate the probability that a sick life goes into state D when he leaves the sick state. (iii) Calculate the expected future lifetime of a healthy life.The number of claims arising in a year on a certain type of insurance policy has a Poisson distribution with parameter 1. The insurer's claim file shows that claims were made on 238 policies during the last year with the following frequency distribution for the number of claims: Number of claims Frequency 174 50 AWN- 10 4 25 No information is available from the policy file, that is, only data concerning those policies on which claims were made can be used in the estimation of the claim rate 1 (This is why there is no entry for the number of claims being 0 in the table.) (i) Show that the truncated probability function is given by: P(X = x)= x = 1,2,3. ... x!(1-e-4) (ii) Hence show that both the method of moments estimator and the MLE of 1 satisfy the equation 1 = x(1-e-*) , where & is the mean number of claims for policies that have at least one claim. (iii) Solve this equation, by any means, for the given data and calculate the resulting estimate of 1 to two decimal places. (iv) Hence, estimate the percentage of all policies with no claims during the year.A car manufacturer runs tests to investigate the fuel consumption of cars using a newly developed fuel additive. Sixteen cars of the same make and age are used, eight with the new additive and eight as controls. The results, in miles per gallon over a test track under regulated conditions, are as follows: Control 27.0 32.2 30.4 28.0 26.5 25.5 29.6 27.2 Additive 31.4 29.9 33.2 34.4 32.0 28.7 26.1 30.3 If we is the mean number of miles per gallon achieved by cars in the control group, and is the mean number of miles per gallon achieved by cars in the group with fuel additive, test: (i) Ho:HA -HC =0 vs H1:HA-HC>0 (ii) Ho: MA- HC =6 VS H1 : HA -HC #6