Chapter 6: Problem 3

An indifference curve is convex to the origin'. Comment.

Short Answer

Expert verified

Answer: When we say that an indifference curve is convex to the origin, it means that the shape of the curve bows outward away from the origin of the graph, indicating that consumers generally prefer diversified bundles of goods over extreme or one-sided combinations. This convexity is due to the assumption of diminishing marginal rate of substitution between the two goods, where as a consumer consumes more of one good, their willingness to give up the other good to get even more of the first good decreases.

Step by step solution

Understand the concept of an indifference curve

An indifference curve is a graphical representation of various combinations of two goods that give a consumer equal satisfaction and utility. Each point on an indifference curve represents a different combination of the two goods such that the consumer is indifferent between them, i.e. they derive the same level of satisfaction from all such combinations.

Define 'convex to the origin'

'Convex to the origin' means that the shape of the curve bows outward away from the origin of the graph. It is a basic property of normal indifference curves that indicates consumers generally prefer diversified bundles of goods over extreme or one-sided combinations of the goods.

Explain the reason behind the convexity of indifference curves

Indifference curves are convex to the origin due to the assumption of diminishing marginal rate of substitution (MRS) between the two goods. MRS is the rate at which a consumer is willing to give up one good to get more of the other good while maintaining the same level of satisfaction. As the consumer consumes more of one good, their willingness to give up the other good to get even more of the first good decreases. This is because they have enough of the first good, and now they desire more of the other good. This diminishing MRS results in the convex shape of the indifference curve.

Show the convexity using a graph

To illustrate the convexity of an indifference curve, create a graph with Good 1 on the x-axis and Good 2 on the y-axis. Draw an indifference curve, such as a downward-sloping oval shape that is bowed outward away from the origin. The curve should start from the upper left corner (where the consumer consumes only Good 2) and extend to the lower right corner (where the consumer consumes only Good 1). The convex shape of the curve represents the diminishing MRS between the two goods.

Comment on the statement

The statement "An indifference curve is convex to the origin" is a correct representation of the general property of indifference curves under normal circumstances, where consumers have a preference for diversified bundles of goods and have a diminishing marginal rate of substitution between the two goods.