Question

Given a worker with 8hours shift, where each hour of effort produce 3 widgets
The price rate of one widget produced is $5 , also given the persians
Utility(s, m)=s^1/3 m^2/3. Where s is shirking and m is salary
Find the hours of shirking and income

Answer 1

To find the hours of shirking and income, we need to maximize the utility function U(s, m) while taking into account the worker's effort and the price rate of the widgets produced.

Let's start by calculating the total number of widgets the worker can produce in an 8 hours shift:

Number of widgets produced = Hours of effort * Widgets produced per hour
Number of widgets produced = 8 hours * 3 widgets/hour
Number of widgets produced = 24 widgets

Now, let's calculate the income the worker will receive from selling these widgets:

Income = Number of widgets produced * Price rate per widget
Income = 24 widgets * $5/widget
Income = $120

Next, we can use the utility function U(s, m) to determine the amount of hours the worker will shirk and the corresponding salary. To maximize the utility function, we need to find the values of s and m that maximize the function's value.

However, the utility function given – U(s, m) = s^(1/3) * m^(2/3) – is not directly dependent on the hours of shirking (s). This means that no matter how many hours the worker shirks, it won't affect the utility value. As a result, we cannot determine the specific hours of shirking from the given utility function.

All we can determine from the information provided is that the worker will receive an income of $120 for an 8 hours shift.