2. An economy consists of two consumers with labels i=1,2. They exchange two goods labelled j=1,2....

 

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2. An economy consists of two consumers with labels i=1,2. They exchange two goods labelled j=1,2. Suppose there is a fixed total endowment e; of each good to be distributed between two consumers. Let c denote i's consumption of good j. Suppose that each consumer i has preference represented by the utility function U¹(c{,c²) = α₁lnc{ + a₂lncź where the parameters a¡ are positive and independent of i, with α₁ + α₂ = 1. Suppose the goods are to be distributed in order to maximize social welfare in the form of the weighted sum W = B₁U¹ + B₂U² where I are positive and B₁ + B₂ = 1 2-A) Formulate the welfare maximization problem with one equality constraint for each of the goods. 2-B) Write down the Lagrangian where λ; denotes the Lagrange multiplier associated with the constraint for good j. Find the welfare maximizing distribution of the goods. aw* 2-C) Verify that λ₁ where W* denotes the maximum value of W. 2 деј = 2. An economy consists of two consumers with labels i=1,2. They exchange two goods labelled j=1,2. Suppose there is a fixed total endowment e; of each good to be distributed between two consumers. Let c denote i's consumption of good j. Suppose that each consumer i has preference represented by the utility function U¹(c{,c²) = α₁lnc{ + a₂lncź where the parameters a¡ are positive and independent of i, with α₁ + α₂ = 1. Suppose the goods are to be distributed in order to maximize social welfare in the form of the weighted sum W = B₁U¹ + B₂U² where I are positive and B₁ + B₂ = 1 2-A) Formulate the welfare maximization problem with one equality constraint for each of the goods. 2-B) Write down the Lagrangian where λ; denotes the Lagrange multiplier associated with the constraint for good j. Find the welfare maximizing distribution of the goods. aw* 2-C) Verify that λ₁ where W* denotes the maximum value of W. 2 деј =

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Q 2A welfare Maxn for Good 1 2B for Good 1 FOC ah h 092 for Good2 FOC 1 1 4 2 Inc 2 in c 4 lnc L... View the full answer