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Consider Sarah’s utility function: ?(?, ?) = ? + ?^1/2 a. Write down the lagrangian for...

Consider Sarah’s utility function: ?(?, ?) = ? + ?^1/2

a. Write down the lagrangian for Sarah’s utility maximization problem. Use the usual budget constraint. ii. What are the three first order conditions from the maximization problem? iii. Solve for the Marshallian demand functions of X and Y.

b. Suppose that Sarah’s income is $10 and Px=2 and Py=1. She learns about a new store in town in which she pays a fee of $2 but then she can buy all the X she wants at a price of just $1. Would Sarah be willing to pay the fee to shop at the new store?

c. Write down Sarah’s cost minimization problem. ii. What are the first order conditions for this problem? iii. Solve for the Hicksian demand functions. iv. What is the expenditure function?

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