Answer to Question #224777 in Economics for jay

Question

Max is a utility-maximizer consumer with a utility function U (x , y )=x+√ y and the usual budget

constraint M=px

x+ p y

y , where M is his income, px and py is the price of good x and y,

respectively.

1. Write down Max’s optimization problem as an optimization problem with a single variable, y.

(Hint: solve the budget constraint for x, and plug the solution for x into the objective function.

2. Write down Max’s first order condition(s) for an interior solution.

3. Use the Implicit Function Theorem with the first order condition to calculate all the partial

derivatives of the optimal value of y. Note: you have to calculate these derivatives without

calculating the optimal value of y!

for which values of prices and income are they possible?

7. Write down Max’s optimization problem as a constrained optimization problem.

8. Write down the first order conditions for Max’s constrained optimization problem.

Answer 1

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