Problem $4$ Assume that you are a real estate broker with an exclusive contract $-$ the condo

association rules state that everyone selling their condominiums must go through you or a broker

designated by you. A typical condo costs $$500,000$ today and sells again every $5$ years. Assume

the first sale will happen in $5$ years. This will last for $50$ years, and then all bets are off. Your

commission will be $3\%.$ Condos appreciate in value at a rate of $2\%$ per year. The interest rate is

$10\%$ per annum.

a$.$ What is the value of this exclusivity rule for one condo? In other words, at what price should

you be willing to sell the privilege of being the exclusive representation for one condo to

another broker?

b$.$ If free Internet advertising was equally effective and if it could replace all real$-$estate agents

so that buyers' and sellers' agents would no longer earn the traditional $6\%(3\%$ each$),$ what

would happen to the value gain of the condo?