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#### Romeo's preferences for pizza (good 1) and pasta (good 2) are represented by the utility function u(xR, 2) = 2xR + < Juliet's utility function is given by u'(x,x) = x+2) Romeo's initial endowment consists of 4 pizzas and 2 portions of pasta whereas Juliet's initial endowment consists of 2 pizzas and 4 portions of pasta

###### Economics

Romeo's preferences for pizza (good 1) and pasta (good 2) are represented by the utility function u(xR, 2) = 2xR + < Juliet's utility function is given by u'(x,x) = x+2) Romeo's initial endowment consists of 4 pizzas and 2 portions of pasta whereas Juliet's initial endowment consists of 2 pizzas and 4 portions of pasta.

(a) Draw an Edgeworth box for this exchange economy with two consumers. Indicate the point of initial endowments and sketch several indifference curves for both individuals. Show the allocations that form the set of mutually beneficial exchanges (lens of exchange).

(b) Calculate the marginal utilities of both consumers with respect to both goods. Then calculate each consumer’s marginal rate of substitution between pizza and pasta. Write down the general condition for a Pareto-efficient allocation in the interior of the Edgeworth box, i.e. if both individuals consume positive amounts of both goods. Make a conclusion whether it Romeo and Juliet may both consume positive amounts of both goods in a Pareto optimum.

(c) Now consider possible Pareto-efficient allocations on the boundary of the Edgeworth box, i.e. whenever at least one individual consumes only one of two goods. By considering Romeo and Juliet’s preferences, determine the set of all Pareto-efficient allocations and draw the contract curve. (Hint: no algebraic calculation is necessary, graphical and logical reasoning is sufficient.) Use the 1st fundamental theorem of welfare economics to find graphically the range of possible market equilibria given the initial endowment in this economy.