Final answer:
Without specific rates for the babysitters, we cannot calculate the exact number of hours after which they would make the same amount. For Vivian, an increase in wage to $12 per hour could influence her work hours based on her preference for leisure versus income.
Step-by-step explanation:
To determine after how many hours competing babysitters would make the same amount, we need to establish their respective hourly rates and then set up an equation where the earnings would equal each other. However, the question does not provide specific rates, so we cannot calculate this directly. We can only say that the point at which two babysitters would make the same amount is the point where their earnings intersect when plotted on a graph.
As for Vivian's scenario, when her wage increases to $12 per hour, this could affect her choice of how many hours to work. A higher wage typically tilts the budget constraint up more steeply because for every hour worked, Vivian earns more. This can allow her to either work the same number of hours and enjoy more income or choose to work fewer hours while maintaining her original income level. With the new wage, her decisions can be based on her preference for leisure versus income.