Assume two consumers with utility functions of the form 1/2 1/2 UX (x₁, x₂) = x/²x/² and UX (y₁, 92) = 91Y2. Further, suppose that consumer X is endowed with wx = (6,2) and consumer Y with w = (2,6). Question 5. Assume the consumers face prices p = (1, 1). Determine the net demands for each consumer. Question 6. Assume the situation of an exchange economy. (a) Determine the contract curve as an expression in which good 1 (₁) is a function of good 2 (x₂). (b) Provide a diagram that illustrates the contract curve and the core of the economy. (c) Determine the Walrasian equilibrium prices.
Assume two consumers with utility functions of the form 1/2 1/2 UX (x₁, x₂) = x/²x/² and UX (y₁, 92) = 91Y2. Further, suppose that consumer X is endowed with wx = (6,2) and consumer Y with w = (2,6). Question 5. Assume the consumers face prices p = (1, 1). Determine the net demands for each consumer. Question 6. Assume the situation of an exchange economy. (a) Determine the contract curve as an expression in which good 1 (₁) is a function of good 2 (x₂). (b) Provide a diagram that illustrates the contract curve and the core of the economy. (c) Determine the Walrasian equilibrium prices.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Q7
Transcribed Image Text:For Questions 5-7 below, consider the following description of a two-goods example:
Assume two consumers with utility functions of the form
1/2 1/2
UX (x₁, x₂) = x/²x² and UX (y₁, 92) = y1Y2.
Further, suppose that consumer X is endowed with wx = (6,2) and consumer Y with w = (2,6).
Question 5. Assume the consumers face prices p = (1, 1). Determine the net demands for each
consumer.
Question 6. Assume the situation of an exchange economy.
(a) Determine the contract curve as an expression in which good 1 (₁) is a function of good 2
(T₂).
(b) Provide a diagram that illustrates the contract curve and the core of the economy.
(c) Determine the Walrasian equilibrium prices.
Question 7. Provide general formulations of the First and Second Welfare Theorems for an ex-
change economy and, using the specific exchange economy of this section, illustrate the theorems
in a diagram.
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