Question

A consumer with the utility function U(X, Y) = [X – 10] Y^(1/2) with an income of $100 to spend on good X (with price $1) and good Y (with price $15).

1 Express this consumer’s utility maximization problem, using the particulars of this problem.

2 Give two conditions that the consumer’s optimal bundle will satisfy, again using the particulars of this problem.

3 Find the two conditions for the consumer’s optimal bundle. Neatly show your work.

4 Find the demand function for good X for a consumer with the given utility function. In other words, resolve this problem only now leaving the prices and income as variables: pX, pY, and m. Neatly show your work.