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{"ops":[{"insert":"Max is a utility-maximizer consumer with a utility function U (x , y )=x+\u221a y and the usual budget\nconstraint M=px\nx+ p y\ny , where M is his income, px and py is the price of good x and y,\nrespectively.\n1. Write down Max\u2019s optimization problem as an optimization problem with a single variable, y.\n(Hint: solve the budget constraint for x, and plug the solution for x into the objective function.\n2. Write down Max\u2019s first order condition(s) for an interior solution.\n3. Use the Implicit Function Theorem with the first order condition to calculate all the partial\nderivatives of the optimal value of y. Note: you have to calculate these derivatives without\ncalculating the optimal value of y!\n\nfor which values of prices and income are they possible?\n7. Write down Max\u2019s optimization problem as a constrained optimization problem.\n8. Write down the first order conditions for Max\u2019s constrained optimization problem.\n\n"}]}
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