1. For the following utility functions,

• Find the marginal utility of each good.

• Determine whether the marginal utility decreases as consumption of each good increases (i.e., does the utility function exhibit diminishing marginal utility in each good?).

• 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.

• Graph the indifference curve where utility is equal to a value of 100.

a. U(X,Y) = 5X + 2Y

b. U(X,Y) = X 0.33 Y 0.67

c. U(X,Y) = 10X 0.5 + 5Y