Question

Explain why an indifference curve is downward sloping and convex to the origin.

Hint:

Indifference curves are downward sloping and convex due to the diminishing marginal rate of substitution. This shows how a consumer substitutes between goods to maintain the same level of satisfaction.

Answer 1

Step 1: Defining Indifference Curves:
An indifference curve represents all combinations of two goods that give a consumer the same level of satisfaction or utility. The consumer is indifferent between these combinations because they provide the same satisfaction.
Step 2: Downward Sloping Indifference Curve:
An indifference curve is downward sloping because as the consumer increases the quantity of one good, they must reduce the quantity of the other good to maintain the same level of utility. This reflects the trade-off or substitution effect between the two goods. If the consumer increases consumption of one good, they are willing to give up some of the other good to maintain their overall satisfaction.
Step 3: Convexity to the Origin:
An indifference curve is convex to the origin because of the law of diminishing marginal rate of substitution (MRS). As the consumer substitutes one good for another, they are willing to give up fewer units of the good they have in abundance to gain an additional unit of the good they have in lesser quantity. This diminishing willingness to substitute leads to the convex shape of the curve.
Step 4: Final Conclusion:
Indifference curves are downward sloping due to the trade-off between two goods, and they are convex to the origin due to the diminishing marginal rate of substitution. These characteristics reflect the consumer's preferences and the principle of substitution.