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Question-3 Suppose the consumer’s utility function is given by U (x1 , x2 ) = x1x...

Question-3 Suppose the consumer’s utility function is given by U (x1 , x2 ) = x1x 2 2 . Let the prices of good 1, good 2 be p1 , p2 , and suppose this consumer wants to reach a level of utility U

(a) [2] Formulate the consumer’s problem in terms of the Lagrangian

(b) [5] Derive the Hicksian demands for this consumer

(c) [3] What is the expenditure for this consumer.

(d) [5] Show that x H ( p1 = 1, p2 = 2, U⋆ = from (c) in question 2) = x M (p1 = 1, p2 = 2, 10) from part (a) of question 2

(e) [5] Suppose originally p1 = 1, p2 = 2, U = 27. The government imposes a quantity tax on good 1 equal to $1 per unit.In the following graph illustrate the original and the after tax solutions to this consumer’s problem. Clearly identify all relevant points of the solution

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Civen the Equations Ans! utility function = u(xir x2] = = xixa. goody good 2 = Pur Pz. i a) minimize = Pix, + P2 X₂ x, x2 = 0> K, :. → Hicksían deinend of te 42,2 Y - Hicksiau Demand of x₂ Expendi terår- Consumed (E) = Pix, + P2 X 2 12 24 Des (1083

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