Brenda Stowers is a licensed real estate agent in the Sedona, Arizona area. Because of her affiliation with a large national real estate agency and her attention to detail, Brenda has been able to build a very successful business. In the United States, people selling their home hire an agent who "lists" the home. The agent representing the potential buyers "shows" the home. If a sale occurs, the seller pays a commission to both the agent listing the house (i.e., their own agent) and the agent representing the buyers. Each agent typically receives a commission equal to 3% of the home's selling price. On occasion, the listing agent is also the agent for the buyer. In this case, the listing agent receives both commissions; that is, as the agent for both the buyer and the seller, the agent receives a total commission of 6%.

On behalf of an owner, Brenda currently has listed a home with an asking price of $250,000. Brenda believes that if she holds an open house this coming Sunday, the home will attract many visitors. (An open house is a designated period, say 2-4 p.m, when the house is open to visitors. Anybody can walk into the house and look around without a prior appointment). Since this is a new listing, Brenda believes that there is a 10% chance one of the visitors to the open house actually will purchase the house. The prep for the open house plus the time it takes to host the open house will consume an entire day. In addition, variable costs related to signs and ads in the local newspaper will cost Brenda $250. Finally, almost all buyers who look at open houses are likely to be under contract with another realtor, implying that Brenda expects to receive a 3% commission if the home sells.

Alternatively, Brenda could spend this coming Sunday showing homes to some of her clients who are looking to buy a house. Brenda estimates that, on any given day that she devotes to showing homes, there is a 4% chance that she will sell a house that is not her listing (thereby receiving a 3% commission), and a 1% chance that she will sell a house that is her listing (thereby receiving a 6% commission). The average asking price of the houses Brenda shows is $220,000. Brenda's variable costs of showing homes are negligible and, thus, can be ignored. Finally, on average, houses (including open houses) sell for 95% of the asking price.

Required:

a. Does Brenda's decision deal with excess supply or excess demand?

b. What is Brenda's expected profit from holding the open house this coming Sunday?

c. What is Brenda's expected profit from showing homes (to some of her clients who are looking to buy a house) this coming Sunday?

d. What should Brenda do this coming Sunday?

e. As you might suspect, the chances of selling a home during an open house decline after the first open house. Assume Brenda's first open house does not lead to a sale.

What would the chances of a sale during the second open house need to be so that Brenda prefers holding a second open house rather than showing homes to potential buyers (assume everything but the chance of sale remains the same)?