improve profitability

Incentive Pay at Handmade Scarves
Individual artisans make fashionable scarves at Handmade Scarves. Each scarf sells for a price of $50. On average one hour of effort will produce one additional scarf.

The monetary value (in dollars) of an artisan's output of scarves (Q) per period is a function of the artisan's level of effort (e) and a random variable (u) with mean 0:

Q = 50e + u

The last term denotes the effect of outside risk factors on scarf production, and has the following distribution: u= +95 with probability 0.50 and u= -95 with probability 0.50. (in dollars)

Your predecessor observed that workers must obtain a level of utility of at least 150 or else they leave for better opportunities at another firm. Your predecessor had established the following human resource policy. Each artisan is paid a base salary of $950 and $30 (or 60% of the value) for each scarf that they produce.

Unfortunately, as a manager for Handmade Scarves you are unable to monitor the actual level of effort chosen by each of your artisans. An artisan has an effort cost of C = 3 e2, where e is the level of effort. (That is not a typo, scarf production is so tiring that the cost of effort to an artisan is C = 3e2.) Therefore the current compensation contract (per period) is W=$950 + 0.6*Q, where Q is the monetary value of scarves produced by the artisan.

a. Based on the above information, how many hours of effort will each artisan supply, given that an artisan maximizes the expected value of her utility. Her utility function equals her monetary compensation less her cost of effort. You may create a table such as the one started for you on the next page.

b. What is the expected value of profits per employee for Handmade Scarves under the above human resources policies?

c. As the owner of Handmade Scarves, I fired your predecessor. Why? How would you change the human resource policies to improve profitability? Please be as specific as possible.

Effort hours e
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