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.

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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.
b) Jack has a monthly income of PhP 1,000 and this is just 50% of what Peter receives
every month. Meanwhile, the prices of apples are around 5% of Jack's income and you
can buy oranges with half the price of apples. Given this, determine the optimum number
of apples and oranges that Jack and Peter can buy, given the goods' prices and their
respective income.
c) Given the optimal number of apples and oranges that they intend to buy, what is the
maximum 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 Jack
and 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, what
will be the number of apples and oranges that they will buy, given that the price of orange
and Jack's income is still the same? Find the new X*, Y*, U* and 2*. Interpret your answer
and present in a graph.
f) Based on your answers a, b and c, present the endowments of Jack and Peter in
consuming apples and oranges through an Edgeworth box. Label correctly and present
the equilibrium points.
g) Based on f, determine the set of Pareto-Improvement allocations. Discuss the possible
scenarios 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 an
Edgeworth box. Interpret your answer and discuss the possible scenarios that will be
experienced by Jack and Peter, with respect to their preferences in both goods.
Transcribed Image Text: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. b) Jack has a monthly income of PhP 1,000 and this is just 50% of what Peter receives every month. Meanwhile, the prices of apples are around 5% of Jack's income and you can buy oranges with half the price of apples. Given this, determine the optimum number of apples and oranges that Jack and Peter can buy, given the goods' prices and their respective income. c) Given the optimal number of apples and oranges that they intend to buy, what is the maximum 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 Jack and 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, what will be the number of apples and oranges that they will buy, given that the price of orange and Jack's income is still the same? Find the new X*, Y*, U* and 2*. Interpret your answer and present in a graph. f) Based on your answers a, b and c, present the endowments of Jack and Peter in consuming apples and oranges through an Edgeworth box. Label correctly and present the equilibrium points. g) Based on f, determine the set of Pareto-Improvement allocations. Discuss the possible scenarios 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 an Edgeworth box. Interpret your answer and discuss the possible scenarios that will be experienced by Jack and Peter, with respect to their preferences in both goods.
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