3. You want to sell your house for SV by hiring a realtor. A realtor can sell yo

Question

3. You want to sell your house for SV by hiring a realtor. A realtor can sell your property with zero effort if the market is "good". If the market is "bad" she can sell only the market is bad by exerting effort at cost C. You cannot tell the actual market condition but you now that it is good with probability a. Write an optimal contract(s) for the realtor based on the values of V, C, and (the optimal contract depend on the relative values of the parameters). b. What your losses due to your inability to directly observe market condition? (the answer should be written in terms of the parameters V, C, and

Explanation / Answer

(a)

Let 'p' be the commission proportion of 'V' written by the realtor in the contract. So, the charge by the realtor is p.V. Consider the following payoff matrix for the realtor.

According to the above payoff matrix, the realtor will only form a contract when the expected payoff is better than staying out of the deal. In other words,

p.V. + (p.V - C).(1 - ) > 0
or, p.V - C + C. > 0
or, p > C.(1 - ) / V

Therefore, the optimal contract should have a commission (p) greater than C.(1 - ) / V to have the contract realized to be attractive. In other words, she should quote a rate = p.V = C.(1 - )

(b)

When the market condition would be known, I could have entered the contract only when the market is good. So, my expected payoff with perfect information would have been -

V. + 0.(1- ) = V

So, the loss is V - C.(1 - )

States of nature Expected
net payoff Alternatives Good market Bad market Form Contract p.V p.V - C p.V. + (p.V - C).(1 - ) Stay out of the deal 0 0 0 Probability 1 -

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