Suppose your book consists of blue and red cars with the following metrics: Blue cars Red cars Loss Expenses Elasticity Quote volume Close rate Price 300 60 2 2000 40% 500 350 50 4 1000 30% 500 a. Find prices that maximize profit dollars b. Do these prices agree with your derivation in #1? Why or why not? c. Maximize profit subject to the constraint that no volume is lost. d. Maximize volume subject to the constraint that no profit is lost. Definitions: Profit= (Price-Costs)" (Policy Count); Margin (which is profit percentage or ratio) = (Price-Costs)/Price Costs losses + expenses Strike rate: Percent of offers accepted, called close (or hit or conversion) rate for new business and retention for renewals. We'll take strike rate to be a function of price in these problems, Elasticity: -(% change in strike rate) / (% change in price) = - S'P Be careful of negative signs! Elasticity is written as a positive number though it measures an inverse relationship. Please note that these problems illustrate relevant mathematical concepts but do not represent real pricing practices which are more complex and subject to a variety of regulatory and professionalism constraints. Note: Unless otherwise directed, treat elasticity in a "simple" manner. If price is currently $100, volume 1000, and elasticity 2, then a 10% drop in price to $90 increases the volume by 20% (-2*10%) to 1200. On the other hand, if you drop the price first to $95 and then $90 and use an elasticity of 2 in each step, you'd get a volume of -1216. Elasticity is a point estimate and doesn't actually apply to every jump in price.