11.12.2024,11:07 Question 1 Not yet answered Marked out of 30.00 Consider the following pure exchange economy with two consumers and two goods, I and y Consumer's utility functions are given by u_(1)(x,y)=min 2x,y and u_(2)(x,y)=(x+y-1)^2+sqrt (10) Suppose that the initial endowments of Consumer 1 and Consumer 2 satisfy omega _(1)+omega _(2)=(2,2) Instructions: If you answer is not an integer,round your answer to 2 decimal places (for example, 1/3 is 0.33,1/2 is 0.5 and 2/3 is 0.67). __ First suppose that the initial endowments of Consumer 1 and Consumer 2 are omega _(1)=(1,1) and omega _(2)=(1,1) Normalize prices in this economy such that p_(x)=pgeqslant 0 and p_(y)=1 For each p below.calculate demands of both consumers for both goods and identify whether the resulting profile constitutes a Walrasian equilibrium. for p=1/2 x_(1): y_(1):square x_(2):square y_(2): square Is it a WE equilibrium? Yes No for p=2 x_(1): y_(1):square x_(2):square y_(2): square Is it a WE equilibrium? Yes No Pure Exchange Economy

To determine the demands of both consumers for both goods and identify whether the resulting profile constitutes a Walrasian equilibrium, we need to solve the consumer optimization problems for each consumer given the price vector p.For Consumer 1: The consumer aims to maximize their utility subject to their budget constraint. The budget constraint is given by: Substituting the given values, we have: Simplifying, we get: The consumer's optimization problem is: subject to: The consumer will choose the bundle such that . Substituting this into the budget constraint, we get: Solving for x, we get: Substituting this back into , we get: Therefore, Consumer 1's demand for good x is and for good y is .For Consumer 2: The consumer aims to maximize their utility subject to their budget constraint. The budget constraint is given by: Substituting the given values, we have: Simplifying, we get: The consumer's optimization problem is: subject to: The consumer will choose the bundle such that . Substituting this into the budget constraint, we get: Solving for y, we get: Substituting this back into , we get: Therefore, Consumer 2's demand for good x is 0 and for good y is .Now, let's check if the resulting profile constitutes a Walrasian equilibrium. A Walrasian equilibrium occurs when the demands of both consumers for both goods are such that the market clears, meaning that the total demand for each good equals the total supply.In this case, the total demand for good x is and the total supply is 2. The total demand for good y is and the total supply is 2. Since the total demand for both goods does not equal the total supply, the resulting profile does not constitute a Walrasian equilibrium.Therefore, the answer is:for Is it a WE equilibrium?No