Q.Discuss the relationship between total utility and marginal utility, using a hypothetical schedule.

Total utility is the total satisfaction a consumer derives from consuming a given quantity of a commodity, while marginal utility is the additional satisfaction from consuming one more unit. The two are linked: marginal utility is the change in total utility when consumption increases by one unit, so $MU_n = TU_n - TU_{n-1}$.

Consider a hypothetical schedule for consuming units of, say, apples:

The Core Intuition

Think of utility as the satisfaction or happiness you derive from consuming a good. When you eat your first slice of pizza after a long day, the pleasure is immense. The second slice? Still great, but not quite as thrilling as the first. By the fifth or sixth slice, you might feel indifferent or even sick. This everyday experience captures the essence of the relationship between total and marginal utility.

Total utility (TU) measures your overall satisfaction from consuming a certain quantity of a good. It's the sum of all the satisfaction you've accumulated from the first unit, the second, the third, and so on.

Marginal utility (MU) measures the change in total utility when you consume one additional unit. Mathematically, it's the difference in total utility between consuming $n$ units and $n-1$ units:

The relationship between the two hinges on a fundamental principle: the law of diminishing marginal utility. As you consume more and more of a good in a given period, the additional satisfaction from each extra unit tends to fall. This doesn't mean you're less happy overall—just that each new unit adds less to your happiness than the one before.

A Hypothetical Schedule

Let's construct a simple example. Suppose you're consuming cups of coffee in a single sitting. Here's how your utility might evolve:

Walk through what's happening. The first cup gives you 20 units of satisfaction—perhaps you were tired and craving caffeine. The second cup adds another 15 units (total utility climbs to 35), but the boost is smaller. By the third cup, you're getting only 10 extra units. The fourth cup adds a mere 5 units; you're approaching satiation. The fifth cup adds nothing—you've hit your bliss point, and total utility plateaus at 50. If you force down a sixth cup, you actually feel worse (jittery, nauseous), so marginal utility turns negative and total utility drops to 45.

Three Key Phases

The schedule reveals three distinct phases in the TU–MU relationship:

Phase I: Rising Total Utility, Positive but Diminishing Marginal Utility

From the 1st to the 4th cup, total utility climbs steadily (0 → 20 → 35 → 45 → 50). Marginal utility is positive throughout (20, 15, 10, 5), meaning each additional cup still adds to your satisfaction, but the increments shrink. Graphically, the TU curve slopes upward but at a decreasing rate—it's concave. The MU curve slopes downward, reflecting diminishing returns.

Phase II: Maximum Total Utility, Zero Marginal Utility

At the 5th cup, total utility peaks at 50 and marginal utility is exactly zero. You've reached the point of satiation: one more unit neither adds to nor subtracts from your well-being. This is the saturation point. In a rational world, you'd stop here.

Phase III: Falling Total Utility, Negative Marginal Utility

Beyond the 5th cup, marginal utility becomes negative (–5 for the 6th cup), and total utility declines (50 → 45). Consuming more now actively harms your satisfaction. The TU curve turns downward, and the MU curve dips below the horizontal axis.

The Mathematical Link …