3. Elaborate the justifications for the negative slope and convexity of indifference curve
The negative slope of an indifference curve is justified by the principle of diminishing marginal rate of substitution (MRS). The MRS is the rate at which a consumer is willing to give up one good in order to obtain more of another good while remaining at the same level of satisfaction. As a consumer consumes more of one good, the satisfaction derived from consuming an additional unit of that good diminishes. Therefore, the consumer becomes less willing to give up units of the other good in exchange for more of the diminishing good. This decrease in the MRS as the quantity of one good increases leads to the negative slope of the indifference curve.
The convexity of an indifference curve is justified by the principle of marginal rate of substitution (MRS) diminishing at a decreasing rate. When a consumer is willing to give up larger and larger quantities of one good in order to obtain smaller and smaller quantities of another good, the MRS is said to be diminishing at a decreasing rate. This occurs when the consumer has strong preferences for one good and is willing to sacrifice relatively more of the other good to obtain additional units of the preferred good. The diminishing rate of substitution is reflected by the convex shape of the indifference curve.
Additionally, convexity of the indifference curve is also justified by the concept of diminishing marginal utility. As a consumer consumes more and more of a good, the additional satisfaction derived from each additional unit of the good decreases. This leads to a diminishing marginal utility. When the marginal utility of one good decreases at a decreasing rate, the consumer is willing to trade off larger quantities of the other good for smaller quantities of the diminishing good. This trade-off creates the convex shape of the indifference curve.
In summary, the negative slope and convexity of an indifference curve are justified by the principles of diminishing marginal rate of substitution and diminishing marginal utility, indicating a consumer's willingness to substitute between goods and the decreasing rate at which additional units of a good provide satisfaction.