Indifference Curves are Convex to the Origin: This is an important property of indifference curves. They are convex to the origin. As the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes as X for Y along an indifference curve.

Indifference curves are convex to the origin because they are based on diminishing marginal rate of substitution.

Explanation:
Indifference curves represent different combinations of two goods that provide the same level of satisfaction to an individual. The shape of an indifference curve reflects the individual's preferences and the trade-offs they are willing to make between the two goods.

Definition of diminishing marginal rate of substitution:
The marginal rate of substitution (MRS) is the rate at which a consumer is willing to substitute one good for another while maintaining the same level of satisfaction. The concept of diminishing marginal rate of substitution states that as a consumer consumes more of one good, they are willing to give up less of the other good in order to maintain the same level of satisfaction.

Convexity of indifference curves:
Indifference curves are typically convex to the origin, meaning they are bowed inward. This convex shape reflects the diminishing marginal rate of substitution.

Visual representation:
If we plot different combinations of two goods on a graph, with one good on the x-axis and the other on the y-axis, the indifference curves will be convex to the origin. This means that as we move along the indifference curve from left to right, the slope of the curve decreases.

Explanation:
The convex shape of indifference curves reflects the concept of diminishing marginal rate of substitution. As a consumer consumes more of one good, they are willing to give up less of the other good to maintain the same level of satisfaction. This is because as the consumer acquires more of one good, the marginal utility derived from each additional unit of that good decreases. Therefore, the consumer is willing to trade less of the other good for more of the first good. This leads to a decrease in the slope of the indifference curve.

Conclusion:
In conclusion, indifference curves are convex to the origin because they are based on the concept of diminishing marginal rate of substitution. The convex shape reflects the consumer's willingness to trade off less of one good for more of the other as they consume more of one good. This shape helps to illustrate the consumer's preferences and the trade-offs they are willing to make between the two goods.