Suppose John's utility function is 4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is given by MUx = 4Y; the marginal utility of Y is given by MUy = 4X.
a. Suppose Y = 3. Calculate John's utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility?
b. Suppose X = 3. Calculate John's utility for Y = 2, 3, 10, and 11. For a given level of X, does good Y display diminishing marginal utility?
c. Find three different bundles containing X and Y that give John 48 utils of satisfaction. Plot the three bundles and connect them with an indifference curve. What happens to the marginal rate of substitution between X and Y as consumption of X increases?
d. Does the principle of diminishing MRS depend on the diminishing marginal utility of X and Y?