2. Statistical discrimination in the market for job insurance

Megasales, Inc. employs 300 salespeople and classifies them annually as either A-Rank (the best), B-Rank, C-Rank, or D-Rank based on the volume of their sales. These rankings determine each salesperson's office size, travel accommodations, and number of days holiday for the following year.

Suppose an insurance dealer approaches the owner of the company and proposes to offer insurance to any salesperson who wishes to secure A-Rank status in the following year. Given the cost of upgrading office size, and so forth, the owner demands $1,000 to promote any salesperson by 1 rank above the rank he or she earns (that is, the owner demands $2,000 to promote one C-Rank salesperson to A-Rank).

The insurer knows the rankings earned by each salesperson in the previous year and also knows that the probability of a salesperson getting demoted by 1 rank in a year is 15%, the probability of being promoted by 1 rank is 15%, and thus, the probability of maintaining the same rank is 70% (with the exception of A-Rank and D-Rank salespeople, who have a 85% chance of maintaining their rank because they can only move in one direction).

Given that a salesperson who earned an A-Rank in the previous year (call this anAPYRankemployee) has a 15% chance of demotion to B-Rank (in which case, it would cost the insurer $___________to pay for the promotion to A-Rank) and a 85% chance of remaining at A-Rank (in which case, it would cost the insurer$_________), the expected cost of insuring oneAPYRanksalesperson is $___________.

Determine the expected cost of providing A-Rank insurance to each category of salesperson (based on last year's rankings). Assuming the insurer can charge different premiums to different ranks of salespeople, enter the value of the premium the insurer should charge toAPYRank ,BPYRank ,CPYRankandDPYRanksalespeople, respectively.

Category of Salesperson Expected Cost of Providing A-Rank Insurance

(Dollars)

APYRank

BPYRank

CPYRank

DPYRank

True or False: Through the use of statistical discrimination, the insurer is able to overcome the problem presented by moral hazard.