Optimal Consumption I). Consider the consumer whose utility function is given by u(x1, x2) = xx,a,>...

  

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Optimal Consumption I). Consider the consumer whose utility function is given by u(x1, x2) = xx,a,ß> 0. Derive the demand for x₁ and x2 when the prices are p₁ and p2, and the income of this consumer is I. Then, using the figure in the next page, draw how the consumption of x₁ depend on income I, when a = 1,ß = 2, and p₁ = P2 = 2. (Your answer should be consistent with Problem 6.) Also in the light of your solution, for what kind of goods consumers (we) are likely to have preference that is captured by Cobb-Douglas utility functions? Your explanation: (2,2,1) 10 1 9 8 7 6 5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100 Income I Optimal Consumption I). Consider the consumer whose utility function is given by u(x1, x2) = xx,a,ß> 0. Derive the demand for x₁ and x2 when the prices are p₁ and p2, and the income of this consumer is I. Then, using the figure in the next page, draw how the consumption of x₁ depend on income I, when a = 1,ß = 2, and p₁ = P2 = 2. (Your answer should be consistent with Problem 6.) Also in the light of your solution, for what kind of goods consumers (we) are likely to have preference that is captured by Cobb-Douglas utility functions? Your explanation: (2,2,1) 10 1 9 8 7 6 5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100 Income I