Do Ollies pay more for left boots more for right boots or an equal price for both?

Gossie has one left boot and Gertie has one right boot. Their values for keeping their boots are vL Show more Gossie has one left boot and Gertie has one right boot. Their values for keeping their boots are vL and vR respectively which take values in the interval [0 1]. Ollie values a pair of boots at vO taking values in [01] and he gets zero value if he has only one or zero boots. (a) Consider the following mechanism. We fix two prices pL and pR. All three goslings announce their values. If vL ? pL and vR ? pR and vO ? pL + pR then both Gossie and Gertie transfer their boots to Ollie and Ollie pays pL to Gossie and pR to Gertie. On the other hand if at least one of the inequalities is violated there is no exchange and there are no transfers. Explain why it is a dominant strategy for each gosling to announce truthfully his/her value. For this question set pL = pR = 1/4. Identify a point (i.e. a list of values (vLvRvO)) in which there are unrealized gains from trade (i.e. no trade takes place despite trade being the efficient outcome.) Let X be the set of points where trade takes place under the mechanism with pL = pR = 1/4. Does there exist a feasible (i.e. incentive compatible and budget-balanced) mechanism which induces trade at all of the points in X and also the point you identified in part 2(a)ii? (b) Suppose now that there are N Gossies N Gerties and N Ollies where N is a very large number. Each Gossie as one left boot each Gertie has one right boot and each Ollie wants a pair of boots. Suppose that the fraction QO(vO) of all Ollies with values for a pair of boots exceeding a given vO is given by: QO(vO) = 1 ? vO and the fractions QL and QR respectively of Gossies and Gerties with values 2 less than given values vL and vR are QL(vL) = vL QR(vR) = (vR)2 Find a mechanism which is incentive compatible budget balanced and realizes all gains from trade. Do Ollies pay more for left boots more for right boots or an equal price for both? Show less

QUICK QUOTE

Approximately 250 words