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Econ 101A — Solution to Midterm 1 Problem 1. Utility ...

Econ 101A Solution to Midterm 1 Problem 1. Utility maximization .(52 points) In this exercise, we consider a standard maximizationproblem with an unusual Utility function. The Utility function isu(x, y)= x+ price of goodxispxand the price of denote income byM,as usual, withM> is well-defined forx>0and fory> now on, assumex>0andy>0unless Compute u/ xand 2u/ the Utility function increasing inx? Is the Utility function concaveinx?(3 points)2. The consumer maximizes Utility subject to a budget constraint. Write down the maximization problemof the consumer with respect the budget constraint is satisfied withequality. (Hint: you can use the answer in point 1) (5 points)3.

The maximization problem is max x,y √ x+ √ y s.t. pxx+pyy≤M. We can write down the budget constraint with equality because the utility function is strictly increasing both inxand y.(Now follows the long explanation, you were not required to give this) As we proved in

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