1 answer

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

Question:

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


Answers

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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