The table below represents a travellers's consumption of bottles of Coca-Cola. Study the table carefully and answer the questions that follow. No. of Bottle...

Answer Details

Marginal utility is the change in total utility from one more bottle: \( MU_n = TU_n - TU_{n-1} \). We use this to fill every gap.

(a) Finding the missing figures

• F (MU of the 2nd bottle) \( = 29 - 15 = \mathbf{14} \).
• Check: MU of 3rd \( = 42 - 29 = 13 \) (agrees with the table).
• D (TU of the 4th bottle): MU is 12, so \( D = 42 + 12 = \mathbf{54} \).
• G (MU of the 5th bottle) \( = 65 - 54 = \mathbf{11} \).
• H (MU of the 6th bottle) \( = 75 - 65 = \mathbf{10} \).
• E (TU of the 7th bottle): MU is 0, so \( E = 75 + 0 = \mathbf{75} \).

(b) The demand curve. Since a consumer buys extra units only if the price falls to match the (declining) marginal utility, plot marginal utility on the vertical axis and quantity of bottles on the horizontal axis, and join the points (1, 15), (2, 14), (3, 13), (4, 12), (5, 11), (6, 10), (7, 0). The curve slopes downward from left to right, which is the traveller's demand curve for Coca-Cola.

(c) Law of diminishing marginal utility. The law states that as more units of a good are consumed, the extra satisfaction from each additional unit falls. In the table MU falls steadily (15, 14, 13, 12, 11, 10, 0). Because a rational consumer pays a price equal to the marginal utility of the last unit, this falling MU means the consumer will buy more only at lower prices, which is exactly why the demand curve slopes downward.