An individual has the utility function, U(X, Y) = 0.5log(X) + log(Y). Let her income be I > 0 and the prices of goods X and Y be Px > and Py > 0.

(a) Determine whether her utility function exhibits increasing, diminishing, or constant marginal rate of substitution.

(b) Prove that her expenditure function is homogenous of degree 1 in prices.

(c) Suppose the price of X increased by 20% but the price of Y decreased by 50%. By what percentage and in which direction should her income change to make her as well off as she was before the change in prices? [Note: DON'T choose numbers for Px and Py].