Risk neutral buyer and seller enter a contract for the

Risk neutral buyer and seller enter a contract for the sale of real estate. The value of the property to the buyer is 500. The seller cannot use the property himself, but he does expect that a third party will appear at some stage after the signing of the contract and offer to buy the property herself. Assume that there is 60% chance that the third party’s offer will be to pay a price of 100, 20% chance that the offer will be 400, and 20% chance that the offer will be 1000. Further, assume that the third party can enter a contract either with the original seller or with the buyer, if the buyer has become the legal owner. Further, if the third party purchases the property directly from the seller, the buyer can then buy it from the third party for a price equal to the price that the third party paid, plus 50. (E.g., if the third party paid 400 to the seller, the buyer can buy the property from the third party for 450) 

(a) Suppose the buyer and seller enter a contract in which the buyer pays 200 upon the signing of the contract and is eligible to receive the property unless the third party offers more- 400 or 1000. If the third party does offer more, the seller does not need to transfer the title to the buyer and does not need to pay the 200 back. Calculate the buyer and seller’s profit under this contract. Show that there is an alternative contract in which the buyer pays a price different than 200 and in which the seller is obligated to supply the property to the buyer even when third party offers 400 (that is, the seller does not need to transfer title to the buyer only when third party offers 1000), and that under this alternative contract both parties are better off. What is the price range that this alternative contract can stipulate? 

(b) Suppose, instead, that the buyer and seller enter a contract in which the buyer pays a price P and is entitled to receive the property unconditionally, irrespective of the third party’s offer. Assume that the remedy in case of breach is specific performance. What is the maximal P that the buyer be willing to pay? How does this price change when the remedy for breach is expectation damages? Liquidated damages of 200? Liquidated (punitive) damages of 2000?

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