1. Alice likes to consume (N + 2) dumplings with each egg she eats. Write the utility function that represents Alice's preferences over dumplings and eggs. Find her demand of dumplings and eggs as a function of her income and the prices of the two goods.
1. Alice likes to consume (N + 2) dumplings with each egg she eats. Write the utility function that represents Alice's preferences over dumplings and eggs. Find her demand of dumplings and eggs as a function of her income and the prices of the two goods.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.1P
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![1.
Alice likes to consume (N + 2) dumplings with each egg she eats. Write
the utility function that represents Alice's preferences over dumplings and eggs. Find
her demand of dumplings and eggs as a function of her income and the prices of the
two goods.
2.
Bob's preferences are represented by the utility function ug(dB, eB)
(N + 1) In(dB) + (eg)². Use the Lagrange method to find Bob's demand of dumplings
and eggs as a function of his income and the prices of the two goods [Note: Try first
to find the demand for eggs and take the positive root of the equation you will obtain].
What would be Bob's demand for dumplings and eggs if the price of dumplings is
Pp = 0.1, the price of eggs is PE = 2 and his budget is mB = 9?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff64a7f68-a8d8-4609-95aa-fce2c58ca2c5%2F38263b56-9ec8-4c08-9781-5f8b9462360e%2F74xoe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
Alice likes to consume (N + 2) dumplings with each egg she eats. Write
the utility function that represents Alice's preferences over dumplings and eggs. Find
her demand of dumplings and eggs as a function of her income and the prices of the
two goods.
2.
Bob's preferences are represented by the utility function ug(dB, eB)
(N + 1) In(dB) + (eg)². Use the Lagrange method to find Bob's demand of dumplings
and eggs as a function of his income and the prices of the two goods [Note: Try first
to find the demand for eggs and take the positive root of the equation you will obtain].
What would be Bob's demand for dumplings and eggs if the price of dumplings is
Pp = 0.1, the price of eggs is PE = 2 and his budget is mB = 9?
Transcribed Image Text:This problem set tells the story of four friends Alice, Bob, C'arol, who are consumers, and
Fanny, who owns a firm. Alice, Bob and Carol have preferences over two goods, Dumplings
and Eggs. Fanny's firm produces eggs. In what follows you should use m; for i = A, B, C to
denote the income of each of the three consumers and p; for j = D, E to denote the prices
of each of the two goods. Similarly, d; and e; denote the consumption of dumplings and eggs
respectively by consumer i = A, B, C. Fanny uses two (non-fixed) inputs, called 1 and 2, to
produce eggs; the price of these inputs is denoted by w; for j = 1,2.
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