For each of the following utility functions,
- Find the marginal rate of substitution,
- Discuss how MRS XY changes as the consumer substitutes X for Y along an indifference curve,
- Derive the equation for the indi?erence curve where utility is equal to a value of 100,
- Graph the indi?erence curve where utility is equal to a value of 100.
(a) U(X,Y ) = XY^2
(b) U(X,Y ) = XY + 10Y
(c) U(X,Y ) = X^2 + Y^2