Question

Let (x1, x2) be some interior bundle on the budget constraint, and suppose p1 = 4 and p2 = 2. If the marginal rate of substitution at (x1, x2) is -3, then is (x1, x2) optimal? Explain why or why not, and justify your answer with economic intuition. (Partial credit for a purely graphical argument.)

Answer 1

Solution:

In consumer theory of economics, for optimal bundle the following condition must hold:

|Marginal rate of substitution of good 1 for good 2| = |p1/p2|

The economic intuition behind this condition is that the rate at which the individual is willing to exchange good 2 for good 1 (MRS) must equal the rate of such substitution allowed in the market (that is it must equal the rate at which market is allowing to make such exchange) (p1/p2). So, only where the two are equal (or slope of indifference curve equals slope of the budget line, or further budget line is tangent to the indifference curve), the optimal bundle is generated as market efficiency is achieved.

Here, |MRS1,2| = |-3| = 3 > 2 = 4/2 = |p1/p2|, that is MRS is greater than p1/p2

This means that at (x1, x2), the rate at which individual is willing to exchange good 1 for good 2 is higher than the rate at which market allows it to do so. So, if the individual still decrease the consumption of good 2 and increase for good 1, the additional satisfaction it derives will be more than the amount it will have to pay for additional units. This further means that the additional satisfaction per cost derived is still higher for good 1, thus at this point, the individual should further consume more of good 1 to reach the optimal point.