For the following utility functions, find the marginal rate of substitution, Discuss how MRS XY

Question:

For 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 indifference curve where utility is equal to a value of 100, and
• Graph the indifference curve where utility is equal to a value of 100:
a. U(X,Y) = XY2
b. U(X,Y) = XY + 10Y
c. U(X,Y) = X2 + Y2