Basic Supply and Demand and Some Factors Affecting Insurance Supply: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Foundations of Risk Management and Insurance, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Total written premiums, or premiums on all policies written during a certain time period, are often used as an approximation of an insurer's liabilities. The policyholders' surplus, the difference between assets and liabilities, is a measure of how much capital an insurer has to pay greater-than-expected claims (Nyce 2006, p. 7.14).

Premium-to-surplus ratio = (Written premiums)/(Policyholders' surplus).

A lower premium-to-surplus ratio indicates greater insurer financial strength, because fewer written premiums (an estimate of liability) exist for each unit of surplus (an estimate of how much is available to pay greater-than-expected claims).

Source:

Nyce, C.M. Foundations of Risk Management and Insurance (Second Edition). 2006. American Institute for Chartered Property Casualty Underwriters. Chapter 7, pp. 7.9-7.26, 7.34-7.39.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-20-1. Using simple supply-and-demand analysis, determine what happens to quantity sold and price under each of the following circumstances. Assume ceteris paribus (all other things being equal) and a perfect neoclassical market which equilibrates instantaneously.
(a) Supply increases; demand decreases.

(b) Supply decreases; demand increases.

(c) Supply and demand both increase.

(d) Supply and demand both decrease.

Solution S5-20-1. Each of situations has an unambiguous effect on one of the two variables and an indeterminate effect on the other. Draw a supply-and-demand graph to see the effects visually. Here are the answers:

(a) Price unambiguously decreases, while quantity may increase or decrease. Quantity will increase if effect of the supply increase is greater than the effect of the demand decrease.

(b) Price unambiguously increases, while quantity may increase or decrease. Quantity will increase if effect of the demand increase is greater than the effect of the supply decrease.

(c) Quantity unambiguously increases, while price may increase or decrease. Price will increase if the increase in demand exceeds the increase in supply.

(d) Quantity unambiguously decreases, while price may increase or decrease. Price will increase if the decrease in supply exceeds the decrease in demand.

Problem S5-20-2.

Insurer A has total assets of $100 million and total written premiums of $50 million. Insurer B has total assets of $150 million and total written premiums of $120 million. The insurers are otherwise identical. Assume that no other information is available and that the insurers' liabilities have to be estimated using the information given. Using such estimates, what is the absolute value of the difference between the policyholders' surplus of A and the policyholders' surplus of B?

Solution S5-20-2. We use the formula Policyholders' Surplus = Assets - Liabilities.

Here, we are given the assets of each insurer, but we can only estimate liabilities, using total written premiums as a proxy.

Thus, we have the policyholders' surplus estimate for A as $100 million - $50 million = $50 million and the policyholders' surplus estimate for B as $150 million - $120 million = $30 million. The absolute value of the difference between the two surpluses is $20 million.

Problem S5-20-3. Insurer A has total assets of $100 million and total written premiums of $50 million. Insurer B has total assets of $150 million and total written premiums of $120 million. The insurers are otherwise identical. Assume that no other information is available and that the insurers' liabilities have to be estimated using the information given. Using such estimates, what is the premium-to-surplus ratio of each insurer? Which insurer is financially stronger, as measured by this ratio?

Solution S5-20-3. We use the formula Premium-to-surplus ratio = (Written premiums)/(Policyholders' surplus).

From Solution S5-20-2, the policyholders' surplus of A is $50 million, so the premium-to-surplus ratio for A is ($50 million)/($50 million) = 1 = premium-to-surplus ratio for A.

From Solution S5-20-2, the policyholders' surplus of B is $30 million, so the premium-to-surplus ratio for A is ($120 million)/($30 million) = 4 = premium-to-surplus ratio for B.

By this measure, A is financially stronger, since it has a lower premium-to-surplus ratio.

Problem S5-20-4. Give two examples of business practice regulation of insurance companies at the state level.

Solution S5-20-4.

The examples mentioned by Nyce 2006, p. 7.16, include the following:
1. Regulations regarding licensing;

2. Regulations regarding policy language;

3. Regulations regarding minimum financial requirements - such as minimum capital and policyholders' surplus requirements;

4. Regulations regarding marketing practices - which can raise administrative expenses.

There are other possibilities, but any two of the above would suffice to answer the question.

Problem S5-20-5. Give two examples of insurance price regulation of insurance companies at the state level.

Solution S5-20-5.

The examples mentioned by Nyce 2006, p. 7.17, include the following:

1. Prohibitions of certain underwriting factors, such as gender, race, or income, in setting premiums.

2. Limitations on large rate increases in certain lines of insurance - such as private passenger automobile insurance or workers' compensation insurance. (Sometimes state regulators will ask that premium increases per policy renewal be limited to a certain percentage of the original premium - say, 20% or 25%.)

3. Limitations on rates charged for homeowners' insurance in areas susceptible to natural disasters.

There are other possibilities, and the rate regulation practices differ considerably among states, but any two of the above would suffice to answer the question.

See other sections of The Actuary's Free Study Guide for Exam 5.