Experience rating when the company aims to increase the volume of its business

An insurance company aims to increase the volume of its business. The volume is measured by the premium income during one year. The company makes use of N tariff groups. Pn-- premium charged by the company per unit of insurance in tariff group n. qn = premium per unit of insurance in tariff group n corresponding to the statistical experience in the said group. Ln ---- The size of the market in tariff group n. If all insurances in the group pay the same premium and if the company is able to cover the whole of its potential market then Ln is equal to the number of policies. If the premium per policy is equal to Pn times the sum insured and if the company is able to cover the whole of its potential market then Ln is equal to the total sum insured. Fn(p) = the proportion of Ln that actually buys insurance in tariff group n if the company charges the premium p per unit of insurance.