5. Consider an economy with two commodities (x, m) and two consumers, 1, 2. Each consumer...

 

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5. Consider an economy with two commodities (x, m) and two consumers, 1, 2. Each consumer i's consumption is given as (xi,mi) € R+ x R. Each consumer's preferences can be represented by the utility function: ui (xi, mi) = 2√₂ + m₂. The price of commodity 2 is given as p, and commodity m is numeraire. Assume that the endowments of the two consumers are given by: W₁ = (2,0), W₂ = (0,2). (a) Obtain algebraically the set of Pareto-efficient allocations. (b) Draw the curve for the set of its utility possibility frontier. (c) Obtain the aggregate excess demand function of commodity x as a function of p. (d) Obtain the competitive equilibrium price, and the competitive equilibrium allocation. 5. Consider an economy with two commodities (x, m) and two consumers, 1, 2. Each consumer i's consumption is given as (xi,mi) € R+ x R. Each consumer's preferences can be represented by the utility function: ui (xi, mi) = 2√₂ + m₂. The price of commodity 2 is given as p, and commodity m is numeraire. Assume that the endowments of the two consumers are given by: W₁ = (2,0), W₂ = (0,2). (a) Obtain algebraically the set of Pareto-efficient allocations. (b) Draw the curve for the set of its utility possibility frontier. (c) Obtain the aggregate excess demand function of commodity x as a function of p. (d) Obtain the competitive equilibrium price, and the competitive equilibrium allocation.

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SOLUTION a ParetoEfficient Allocations A Paretoefficient allocation is one in which no consumer can be made better off without making the other consumer worse off We can find Paretoefficient allocatio... View the full answer