4. (25 PTS) Consider a consumer whose preference is given by the utility function u(x₁x₂) = x₁ + x₂. The consumer has an

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4 25 Pts Consider A Consumer Whose Preference Is Given By The Utility Function U X X X X The Consumer Has An 1 (21.21 KiB) Viewed 42 times

4. (25 PTS) Consider a consumer whose preference is given by the utility function u(x₁x₂) = x₁ + x₂. The consumer has an income of w and faces prices p and 1 for goods 1 and 2 respectively. Assume pz 1. Goods cannot be consumed in negative amounts and the consumer need not spend all his income. (i) (3 PTS) Write down the optimisation problem of the consumer along with any non-negativity restrictions. (ii) (4 PTS) Prove whether the two conditions for Kuhn-Tucker's theorem satisfied. (iii) (9 PTS) Write down the Lagrange function and find the critical points of this optimisation problem.