Question

1. Explain at least two reasons why economists assume most goods and services are convex to the origin.

2. Use the graph to explain each statement about interior solutions for imperfect substitutes below. In your explanation, make sure you are comparing the marginal utility per dollar spent on each good.

a.) at point a, the consumer should increase their consumption of ?? and decrease their consumption of ??.

b.) at point b, the consumer should not change their behavior.

c.) at point c, the consumer should decrease their consumption of ?? and increase their consumption of ??.

Answer 1

Indifference curves is that they are usually convex to the origin. In other words, the indifference curve is relatively flatter in its right-hand portion and relatively steeper in its left-hand portion. This property of indifference curves follows from assumption that the marginal rate of substitution of X for Y (MRS_xy) diminishes as more and more of X is substituted for Y.

Only a convex indifference curve can mean a diminishing marginal rate of substitution of X for Y.

When the indifference curve is convex to the origin, MRS diminishes as more of X is substituted for Y. We therefore conclude that indifference curves are generally convex to the origin. Our assumption regarding diminishing MRS_xy and the convexity of indifference curves is based upon the observation of actual behaviour of the normal consumer. If indifference curves were concave or straight lines, the consumer would succumb to monomania, that is, he would buy and consume only one good. We know that consumers in actual world do not generally buy and consume one good. It is for this reason that we reject indifference curves of concave or straight-line shapes and assume that indifference curves are normally convex to the origin.

In the above diagram, IC is an indifference curve, and A and B are two points which represent combination of goods yielding same level of satisfaction.

We can see that when X1 amount of commodity X was consumed, Y1 amount of commodity Y was also consumed. When the consumer increased the consumption of commodity X to X2, the amount of commodity Y fell to Y2. And, thus the curve is sloping downward from left to right.