Q3 20 Pointsl Suppose A and B each have 40 units of good X a

Q3: [20 Pointsl Suppose A and B each have 40 units of good X and 40 units of good Y. Ua(X, Y) = X + 2Y, UB (X, Y) 2X + Y. (a) Find all the Pareto-efficient allocations. (b) Solve for the competitive equilibrium. (10,10)

Solution

A. All the combinations of X and y , that gives the same utility to both consumers A and B will give us the pareto efficient allocation. All the units of x and y, where x+2y=2x+y is pareto efficient. This does not mean that A and B should consume 40,40 of x and y. All combinations that give equal satisafaction(points on the same indifference curve) is pareto optmal.

B. equilibrium is determined at the point where the utiity function is tangent to the budget line. since here the prices of goods are mentioned, the equilibrium points cannot be determined.