Final answer:
A higher hourly wage increases the slope of the bid-rent curve by enhancing the workers' ability to pay for land closer to their place of employment, ultimately leading to higher bids for such locations.
Step-by-step explanation:
According to the bid-rent model, a higher hourly wage would theoretically increase the slope of the bid-rent curve. The bid-rent curve represents how much different users are willing to pay for land at varying distances from the city center. When workers earn higher wages, their ability to afford rent at or closer to the city center increases, thus they bid more for locations closer to their work. Therefore, the gradient of what they are willing to pay increases, resulting in a steeper bid-rent curve.
Let's apply this to the example of Vivian. With an increase in her wage to $12/hour, her budget constraint will tilt upwards more steeply. This represents that with higher income, she can afford more, whether it's more leisure time or more hours of work. This is described by different portions of the labor supply curve. The upward-sloping portion suggests that as wages increase, Vivian may choose to work more hours. However, the backward-bending portion suggests that beyond a certain wage level, she might actually choose to work fewer hours, valuing her leisure time more.