Maximilian consumes two goods, x and y.His utility function is U(x, y) maxx, y.Therefore x and y are perfect substitutes for Max.

Maximilian's utility function, U(x, y) = max{x, y}, suggests that his utility is determined by the larger of the two quantities of goods x and y, which is characteristic of perfect complements, not perfect substitutes. In the case of perfect substitutes, the utility function would typically be linear, such as U(x, y) = ax + by.