Esther consumes goods X and Y, and her utility function is U(X, Y) = XY + Y.

Question:

Esther consumes goods X and Y, and her utility function is U(X, Y) = XY + Y.
For this utility function,
MUX = Y
MUY = X + 1.
a. What is Esther's MRSXY? Do her preferences satisfy the declining MRS property?
b. Suppose her daily income is $20, the price of X is $4 per unit, and the price of Y is $1 per unit. What is her best choice? What is the (own) price elasticity of her demand for good Y starting with these prices and income? At what price for good Y is Esther's expenditure on good Y largest?
c. Suppose the price of good Y rises to $4 per unit. What is her new consumption bundle? Decompose the change in her purchases into income and substitution effects. What is Esther's compensating variation for the price change?