# How price is determined in the following monopoly model question?

I am studying microeconomics, and got stuck on the following question, specifically, part (b) and part (c):

A monopoly-owned retail store is located next to a monopoly-owned parking lot. (The store and the parking lot are owned by different monopolists.) Assume:

1. There is a fixed number of customers, all with identical downward-sloping demand curves for the products at the retail store.
2. To shop at the store, you must park in the lot. There is no other reason to park in the lot. Therefore, any customer's willingness to pay for a parking space is equal to the consumer surplus that customer earns from shopping at the store.
3. The store has an upward sloping marginal cost curve.
4. Parking spaces are provided at zero marginal cost.

(a) Suppose the store announces a price, and thuen the parking lot announces a price. Describe (using graphs) how these prices are determined.

(b) Suppose instead that the parking lot announces a price and then the store announces a price. Describe how these prices are determined.

(c) Suppose instead that the prices are announced simultaneously. Describe how they are determined.

This is what I did for part (a). Consider the diagram below. The store is going to set a price first, Since there is no demand curve for the parking lot, the store will not take into consideration the price of the parking lot. The parking lot takes the store's price as given because the parking lot sets its price after the store. Thus, the store will choose the monopoly price where its marginal costs equals its marginal revenue. Then, the parking lot will capture all the consumer surplus, which is area $$A$$. Since there is a fixed number of consumers whose demand curves for goods of the store are identical, the parking lot will set a price equals $$\frac{\text{the area of }A}{\text{the total number of consumers}}$$.

However, I am lost for parts (b) and (c). I really appreciate any help!

The basic idea for part (b), is that if the parking lot goes first to set the price first, the store is going to have to allow the costumers to get at least enough consumer surplus to make it worth for them to come to the store at all. So, consider the following diagram for an example. If the parking lot were to set the price being equal to $$\frac{\text{the area of }A'}{\text{the total number of costumers}}$$, then the store would be forced to charge the costumers the green-line price (i.e., the "store price" in the diagram) for its merchandise, because if it charges anything more than that people would say "I am just not gonna go shopping". So the question is: What is the maximum price the parking lot can set that is consistent with this?
Notice that the store is willing to keep lowering its price until they get down to where there are only negative producer surplus. In the diagram below, suppose that the parking lot sets its price at $$\frac{\text{area of }A + \text{area of }C}{\text{the total number of costumers}}$$. Then, the producer surplus of the store is $$\text{area of }B - \text{area of }C - \text{area of }D$$. Therefore, the parking lot will set its price at some $$\frac{\text{area of }A + \text{area of }C}{\text{the total number of costumers}}$$ such that $$\text{area of }B - \text{area of }C - \text{area of }D = 0$$.