Final answer:
The Gini coefficient for a world with just you and the robot is 1.
There is not perfect equality in this society because one entity (you) earns income while the other entity (the robot) provides a service without earning income, resulting in inequality.
Step-by-step explanation:
First, let's calculate the surplus you gain from renting the robot for a given number of hours.
The surplus is calculated as the value the robot provides minus the cost to rent it.
Given:
- Value provided by the robot = $12 per hour
- Cost to rent = 0.5 * (hour rented)²
If you rent the robot for 'n' hours, your surplus would be:
Surplus = Value provided by the robot - Cost to rent
Surplus = $12 * n - 0.5 * n²
Now, let's consider the earnings and surplus for different scenarios:
If you earn $100 per day (24 hours):
Surplus for 24 hours = $12 * 24 - 0.5 * 24²
Surplus for 24 hours = $288 - 288
Surplus for 24 hours = $0
In this scenario, your surplus is zero, meaning you're spending exactly what the robot provides in value.
Regarding the Gini coefficient and perfect equality, the Gini coefficient measures inequality within a society. In this specific scenario with just you and the robot, the surplus is being shared evenly due to the communist nature of the society.
As the surplus is zero, both you and the robot have the same amount of wealth, resulting in perfect equality (Gini coefficient of 0) within this small society.