Question

Mr. MacGregor's preferences are such that he is indifferent between the following bundles of (x,y): (1,4), (2,2), (4,1). Is it possible that the utility function U In(ry) will represent his preferences? Explain why or why not. Ignoring the utity function, do you think it is likely that he would be indifferent between the previous three bundles and the bundle (2,3)? Why or why not? ::/摄

Answer 1

Given that the consumer is indifferent between the bundles (1,4), (2,2), (4,1) => utility of these bundles is same.

i.e. U = xy = 4 is a valid indifference curve for both.

Using the monotonic transformation property of utility function,

U = ln(xy) = 1.39 will represent consumer's preferences.

This is because all three bundles have same utility in the given form and thus consumer is indifferent between them which matches our information.

Even if we ignore the form of utility function, the bundle (2,3) won't be indifferent to the given bundles.

This is because if we consider(1,4) and (4,1),

the line joining these two points can be stated as:

$y - 1 = \frac{1-4}{4-1}(x-4) = -1(x-4) = 4 -x \Rightarrow x +y = 4$

Bundle (2,2) lies on this line.

Thus for (2,3) to be indifferent to these bundles, it should lie on the line segment which it is not. Thus it doesn't have same utility as the given three bundles.