Solve the constrained optimization problem: max In(co) + In(c) + In (c) CO,C1,C2 subject to poco...

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Solve the constrained optimization problem: max In(co) + In(c₁) + In (c₂) CO,C1,C2 subject to poco + pici + P2₂c2 ≤Y, where In is the natural logarithm function. (1) (2) a. Set up the Lagrangian for the problem. Then write down the first order conditions for choice variables. b. Will the constraint bind or not? Why. c. How the optimal solution depends on ps and Y. d. If we interpret this problem as consumer's optimization problem as follows. A consumer consumes C₁, C₁ and c₂ units of good 0, 1, and 2 in a perfectly competitive market at the unit price po, P₁ and p2. The consumer's objective can be written as Equation (1), and the consumer is subject to the budget constraint of Equation (2), where Y is the total income of the consumer. Then what fraction of the consumer's total income Y does the consumer spend on each good? Solve the constrained optimization problem: max In(co) + In(c₁) + In (c₂) CO,C1,C2 subject to poco + pici + P2₂c2 ≤Y, where In is the natural logarithm function. (1) (2) a. Set up the Lagrangian for the problem. Then write down the first order conditions for choice variables. b. Will the constraint bind or not? Why. c. How the optimal solution depends on ps and Y. d. If we interpret this problem as consumer's optimization problem as follows. A consumer consumes C₁, C₁ and c₂ units of good 0, 1, and 2 in a perfectly competitive market at the unit price po, P₁ and p2. The consumer's objective can be written as Equation (1), and the consumer is subject to the budget constraint of Equation (2), where Y is the total income of the consumer. Then what fraction of the consumer's total income Y does the consumer spend on each good?

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