When real estate agents sell their own, rather than clients', houses, they leave the houses on the market for a longer time (10 days longer on average) and wind up with better prices.

Suppose that real estate agents earn a commission equal to 3% of the sale value of each house that they help sell. Suppose a real estate agent has an offer on a house of $400,000. The agent can get a 5% higher offer with more effort and by leaving the house on the market for a few more weeks.

If the agent sells the house now, he will earn a commission of. By keeping the house on the market and expending more effort to sell the house, the agent can earn a commission of. Thus, the agent gainsf or the extra effort and time of keeping the house on the market.

Suppose a real estate agent has an offer on a house that he owns. The agent has a current offer of $400,000, but can get a 5% higher offer with more effort and by leaving the house on the market for a few more weeks. Assume that all of the commission is paid back to the agent, since he will act as the agent for the sale.

If the agent waits to sell the house, he gains more than selling the house now. Since this amount is than what he would gain by waiting to sell a house he does not own (as in the first part of the problem), the agent is likely to keep a house on the market and expend more effort to sell a house that he owns, as opposed to one that he does not own.