A local clothing retailer currently pays its sales staff a fixed hourly rate of $15 per hour,

Fantastic news! We've Found the answer you've been seeking!

Question:

A local clothing retailer currently pays its sales staff a fixed hourly rate of $15 per hour, which is the prevailing wage for sales staff in this line of work at various clothing stores in NYC. The owner is considering switching to a wage and bonus structure to better incentive her sales staff. She spent some time carefully watching her staff, collecting data, and found the following: on average, five customers come by per hour (with one salesperson working per hour). If a salesperson is attentive and helpful for an hour, each of the 5 customers has a 40% chance of making a purchase, while if the sales staff are otherwise occupied, the chance of each customer making a purchase is 20%. Furthermore, based on her own background and experience, she feels that the “cost of effort” for a salesperson is around $6 per hour. Assume that salespeople are risk-neutral. What is the optimal wage and bonus structure – the lowest possible wage and bonus (per customer who makes a purchase) such that her scheme will result in her sales staff exerting more effort -- to offer her sales staff? Bonus (per customer who makes a purchase): Clothing is a tough market, but the owner estimates she makes a profit margin of $10 per customer that makes a purchase. Is the wage-and-bonus scheme worthwhile for her? Or should she stick with the fixed $15 per hour salary structure (with the understanding that sales staff would not be nearly as attentive and helpful under that approach)? Explain your