# Economics Assignment

Seller supplies only one good to the consumer. Let x be 1 if trade takes place and 0 if not. Let t_{Q} be the amount of money that the seller *receives *and t_{B} the amount that the buyer *pays*. Let v be the buyer’s valuation and s be the seller’s valuation of the object and assume preferences are quasi-linear. We can then normalize utilities so that the seller’s utility is t_{Q} – cx^{2} and the buyer’s utility is vx^{2} – t_{B}. Assume the preference parameters v and c are independently drawn from a uniform distribution on [0,1]. The buyer knows v and the seller knows c.

a. What is the efficient rule for trade?

b. Let m_{S} and m_{B} be the seller’s respectively the buyer’s reported preference for the object. Determine the set of direct mechanisms (expressed as a function of the reports) that admit truth telling as a dominant strategy and implement efficient trade

c. Show that there is a unique Groves mechanism that has the property that whenever trade does not occur, the transfer payments are set equal to zero (t_{B} = t_{S} = 0). Is this mechanism feasible?

d. Show that there is no Groves mechanism for which the budget breaks even for all reported preferences.

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