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# solve all parts. C1 Anne and Bill like strawberries x and chocolate y. Anne starts with an endowment of X kilos outof strawberries and Bill

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## C1 Anne and Bill like strawberries x and chocolate y. Anne starts with an endowment of X kilos of strawberries and Bill starts with an endowment of Y kilos of chocolate. Anne and Bill agree to trade their strawberries and chocolate with each other at prices Px and py respectively. noisibros (a) In an exchange economy, can all agents be made strictly better off if we are already at a Pareto-efficient allocation? If we are not at a Pareto-efficient allocation, can we make all agents strictly better off by trading to a Pareto-efficient allocation? Explain your answers. (b) Assume that the preferences of Anne and Bill are given by the utility function aid) tot ablod u(x, y) = a ln(x - A) + (1 - a) lny, moldog where a and A are constants. Show that if the value of either's endowment is E, then their Jatiladi sedemand for strawberries is A+ a (E-PxA)/Pr atrol (c) Hence, show that the market for strawberries clears if the relative price is tirqlue Lamoiaibazo boog sol bn Px/Py I boog = aY (1-a)(X-2A) (s) Demonstrate also whether the market for chocolate clears at this relative price. (d) Explain intuitively why the equilibrium relative price of strawberries increases as A in- creases. (e) Briefly, in no more than a few sentences, explain the fundamental consequences of the first and second welfare theorem for a government attempting to intervene in a market.

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