A reliable 15-year-old babysitter can be a price maker within her own neighborhood. Suppose that this babysitter wishes to implement a Multipart Pricing Plan. Customers who use her services less than L hours per month will pay a high price of PH dollars per hour. Customers who use her services more than L hours per month will still pay PH dollars for the first L hours, but for any additional hours they can then pay the lower price PL dollars per hour which she will generously set equal to her marginal cost. Assume that market demand is QD = 60 – 10P and her total costs are C = 3Q; so PL = $3 per hour. If she set her high price at $4 per hour, would her customers accept a limit of L = 24 hours per month in order to use the remainder of her services at a price of $3 an hour? Provide a labelled diagram and briefly explain. Suppose that this talented babysitter was also superstar in microeconomics. What values of PH and L should she choose to maximize her profits? Provide a second labelled diagram and briefly explain your results.

P.S. you don't have to draw the diagram but just give me an idea of how to solve the question.

Thanks

To determine if the customers would accept a limit of L = 24 hours per month at a price of $3 per hour, we need to compare the customers' willingness to pay with the cost they would incur with this pricing plan.

First, let's find the demand function by setting the quantity demanded equal to zero and solving for the price:
0 = 60 - 10P
10P = 60
P = 6

So, the maximum price (PH) customers are willing to pay is $6 per hour.

Now, we need to consider the customers who use the babysitter's services for more than L hours. They would pay PH for the first L hours and then PL for the additional hours. The total cost for them would be:
Total cost = PH * L + PL * (Total hours - L)

In this case, the total hours would be 24. Let's calculate the costs for customers who use more than 24 hours per month:
Total cost = 4 * 24 + 3 * (Total hours - 24)
Total cost = 96 + 3 * (Total hours - 24)
Total cost = 96 + 3 * (24 - 24)
Total cost = 96

Now, let's compare the willingness to pay with the cost:
Customers' willingness to pay = PH * L
Customers' willingness to pay = 6 * 24
Customers' willingness to pay = 144

Since the total cost (96) is less than the customers' willingness to pay (144), they would accept the limit of L = 24 hours per month in order to use the remainder of her services at a lower price of $3 per hour.

To determine the values of PH and L that maximize her profits, we need to find the quantity demanded at different price levels, calculate her revenues and costs, and then subtract costs from revenues to obtain her profits. By doing this calculation for different price levels, we can find the combination of prices and limits that yields the highest profit.

We can create a second labeled diagram with the quantity on the x-axis and the price on the y-axis. The demand curve (QD = 60 - 10P) will slope downwards from left to right. The marginal cost curve will be constant at $3 per hour. The profit-maximizing point will be where marginal revenue (MR) equals marginal cost (MC) on the graph.

By finding the price and quantity at the intersection of MR and MC, we can determine the optimal pricing strategy for the babysitter to maximize her profits.

Note: The graphical analysis mentioned above would require actual numerical calculations and plotting, so just a verbal explanation may not be sufficient to provide accurate results.