Photo attached. 1. Jack and Peter lived in a country named Laktoria. The country produces two goods,apples (good x) and oranges (good y). They have unique preferences in buying thesegoods. With this, they have different utility functions in consuming both goods, to wit:Jack: U = 5 x1/3y1/2Peter: U = 7 x1/2y1/3a) In order for us to determine the amount of apples and oranges that Jack and Peterprefer, given their utility functions, we need to derive both of their Marshallian demand inbuying both goods. With this, you need to present the objective, constraint and theLagrange functions for Jack and Peter in consuming apples and oranges. Find theMarshallian demand for apples and oranges.b) Jack has a monthly income of PhP 1,000 and this is just 50% of what Peter receivesevery month. Meanwhile, the prices of apples are around 5% of Jack's income and youcan buy oranges with half the price of apples. Given this, determine the optimum numberof apples and oranges that Jack and Peter can buy, given the goods' prices and theirrespective income.c) Given the optimal number of apples and oranges that they intend to buy, what is themaximum satisfaction level of Jack and Peter in consuming both goods. In addition,determine the amount of utility added in every 1 peso change in income.d) Given you answers in a, b and c, draw the indifference curves and budget lines of Jackand Peter. Present the tangency at the equilibrium point.e) If the price of apple increases by 25% and the income of Peter will be doubled, whatwill be the number of apples and oranges that they will buy, given that the price of orangeand Jack's income is still the same? Find the new X*, Y*, U* and 2*. Interpret your answerand present in a graph.f) Based on your answers a, b and c, present the endowments of Jack and Peter inconsuming apples and oranges through an Edgeworth box. Label correctly and presentthe equilibrium points.g) Based on f, determine the set of Pareto-Improvement allocations. Discuss the possiblescenarios that Jack, and Peter may experience, given their endowments.h) At what quantity of apples and oranges that Jack and Peter are willing to purchase,without being worse off. Find the Pareto-Optimality point. Present this scenario in anEdgeworth box. Interpret your answer and discuss the possible scenarios that will beexperienced by Jack and Peter, with respect to their preferences in both goods.

Thank you for the question, as per Bartleby, we can solve 3 subparts per session.

1. Jack and Peter lived in a country named Laktoria. The country produces two goods, apples (good x) and oranges (good y). They have unique preferences in buying these goods. With this, they have different utility functions in consuming both goods, to wit: Jack: U = 5 x1/3y¹/2 Peter: U = 7 x¹/2y1/3 a) In order for us to determine the amount of apples and oranges that Jack and Peter prefer, given their utility functions, we need to derive both of their Marshallian demand in buying both goods. With this, you need to present the objective, constraint and the Lagrange functions for Jack and Peter in consuming apples and oranges. Find the Marshallian demand for apples and oranges.

1. Jack and Peter lived in a country named Laktoria. The country produces two goods, apples (good x) and oranges (good y). They have unique preferences in buying these goods. With this, they have different utility functions in consuming both goods, to wit: Jack: U = 5 x1/3y¹/2 Peter: U = 7 x¹/2y1/3 a) In order for us to determine the amount of apples and oranges that Jack and Peter prefer, given their utility functions, we need to derive both of their Marshallian demand in buying both goods. With this, you need to present the objective, constraint and the Lagrange functions for Jack and Peter in consuming apples and oranges. Find the Marshallian demand for apples and oranges.

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 1P

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