How can marginal utility theory be utilized to derive the demand curve for a good?

• A. By proving that marginal utility increases as more units of a good are consumed, resulting in an upward-sloping demand curve.
• B. By indicating that the demand curve is vertical because consumers always buy the same quantity regardless of price.
• C. By demonstrating that the demand curve is always perfectly elastic due to constant marginal utility.
• D. By showing that as the price of a good decreases, the consumer can purchase more units, and the marginal utility per dollar spent becomes equal across all goods, leading to a downward-sloping demand curve.

Answer: (D)

Verified step by step guidance

1. Understand the concept of marginal utility (MU), which is the additional satisfaction or benefit a consumer gains from consuming one more unit of a good.
2. Recognize that consumers aim to maximize their total utility given their budget constraint, which means they allocate their spending so that the marginal utility per dollar spent is equalized across all goods. This condition can be expressed as \(\frac{MU_x}{P_x} = \frac{MU_y}{P_y}\), where \(MU_x\) and \(P_x\) are the marginal utility and price of good \(x\), respectively.
3. Analyze how a change in the price of a good affects the quantity demanded: when the price of a good decreases, the marginal utility per dollar spent on that good increases, encouraging the consumer to buy more of it to restore the equality of marginal utility per dollar across goods.
4. Use the law of diminishing marginal utility, which states that as more units of a good are consumed, the marginal utility of additional units decreases. This explains why consumers will only buy more if the price falls, leading to a downward-sloping demand curve.
5. Combine these insights to derive the demand curve by plotting the relationship between the price of the good and the quantity demanded, showing that as price decreases, quantity demanded increases, consistent with the marginal utility theory.