If the agent sells the house now, he will earn a commission of $12,000. By keeping the house on the market and expending more effort to sell the house, the agent can earn a commission of $12,600. Thus, the agent gains $600 for the extra effort and time of keeping the house on the market.
If the agent sells the house now, he will earn 3% on $400,000:
= 400,000 * 3%
= $12,000
If the agent waits, the offer could increase by 5%:
= 400,000 * ( 1 + 5%).
= $420,000
New commission would therefore be = 420,000 * 3% = $12,600
Gain = 12,600 - 12,000 = $600
If the agent waits to sell the house, he gains $20,000 more than selling the house now. Since this amount is more 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 more 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.
If the agent owns the house, the gain is:
= 420,000 - 400,000
= $20,000
This amount is more than the $600 he would gain if the house wasn't his as shown in the first question.
He will therefore most likely wait and expend more effort so he gets this $20,000.
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