Question

Explain why the indifference curve is convex to the origin.

Show that the indifference curve is convex to the origin.

Answer 1

An indifference curve (IC) represents all combinations of two goods that provide a consumer with the same level of satisfaction or utility. The consumer has no preference for one combination over another on the same curve. The indifference curve is convex to the origin because of the Law of Diminishing Marginal Rate of Substitution (DMRS).

The rate at which a consumer is willing to switch from one good to another while still being satisfied is known as the marginal rate of substitution, or MRS.

• The consumer's willingness to give up clothing decreases as they replace more units of clothing (Y-axis) with units of food (X-axis).
• This indicates that as we proceed from left to right along the indifference curve, the MRS falls.
• The curve has a convex form as a result of this decreasing readiness to substitute.

In this diagram:

• Moving from point A to B, the consumer gives up 3 units of clothing to gain 1 unit of food.
• From B to C, they give up 2 units of clothing for 1 more unit of food.
• From C to D, they only give up 1 unit of clothing to gain another unit of food.

This shows that as the consumer consumes more food, the amount of clothing they are willing to give up diminishes, confirming the DMRS and the convex shape of the IC.