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1. A consumer maximizes his utility function, 122, subject to the budget constraint, 75x1 +150x2-525· (M-$75, P2-$150, M-$525). Set up the Lagrangian function and use the first-order and second-order conditions to find the values of x1 and x2 that solve the consumers problem 2. This problem is an extension of Problem 1. Now, the consumer faces an additional constraint. Specifically, good 1 is rationed, and the consumer can buy no more than three units of that good. Thus, he faces an additional (inequality) constraint, 2:1-3. Set up the Lagrangian function and use the first-order conditions and the complementary- slackness conditons to solve the consumers problem. (Dont mess with second-order conditions.)

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