In: Economics
Suppose that there are two consumers A and B and two products x and y. The initial endowment W is such that consumer A is endowed with (WXA, WYA) = (1,8) and consumer B is endowed with (WXB, WXB) = (8,27). Both consumers have standard preferences, and their utility functions are the same and equal to
UA(xA, yA) = xA * yA2 UB(xB, yB) = xB * yB2.
Question 1 -a
Determine consumer A and B’s utility at their initial endowment.
Question 1 - b
Explain how the set of allocations that are Pareto improvements compared to the initial endowment is characterized in an Edgeworth box?
Question 1 - c
What is generally the condition for Pareto efficiency in an economy with two consumers A and B.
Question 1 - d
Determine (mathematically) the slopes of the indifference curves for the two consumers.
Question 1 - e
Determine (mathematically) the equation for the Pareto efficient allocations in the economy described above.