Answer all the questions appropriately

1 "firms in a perfectly competitive market make no profits"

Discuss this assertion.

A simple NCD system for motor insurance has four levels of discount - 0%, 20%, 40% and 60%. A new policyholder starts on 0% discount. At the end of each policy year, policyholders will change levels according to the following rules: At the end of a claim free year, a policyholder moves up one level, or remains on the maximum discount. At the end of a year in which exactly one claim was made, a policyholder drops back one level, or remains at 0%. At the end of a year in which more than one claim was made, a policyholder drops back to zero discount. For a particular driver in any year, the probability of a claim free year is 0.9, the probability of exactly one claim is 0.075, and the probability of more than one claim is 0.025. A policyholder takes out a policy for the first time on 1 January 2004, and by 1 January 2007 he/she had made only one claim, on 3 May 2006. Calculate the probability that he/she is on 20% discount in 2009. [3]Sometimes when no standard mortality table has been produced for female lives, actuaries use the corresponding male table, but apply an "age rating" of 4 years (say), ie they consider a female aged x to be equivalent to a male aged x-4. Explain the rationale underlying this approach. [2]