6) Come up with the formula for a function f(x1; x2), for which you are unable...

6) Come up with the formula for a function f(x1; x2), for which you are unable to draw the indifference map

Expert Solution

Lexicographic preferences cannot be represented by indifference maps. Since lexicographic preferences are not continuous.

In two good situation, if a consumer prefers X over Y then no matter what is the amount of Y he will get he will always prefer X. They are not representable by a utility function.

Note: you can't have one to one mapping between real and rational numbers. However, between any two real numbers there exists at least one rational number.

To show that lexicographic preferences do not utility function:

consider u(x1,0) and u(x1,1). This relationship has a utility function.

We will have u(x1,0) < u(x1,1) using any two real numbers.

We know that between two real numbers we have one rational number - r1

Suppose there are other two bundles - u(y1,0) and u(y1,1) with x1< y1. u(y1,0) and u(y1,1) is greater than u(x1,0) and u(x1,1) due to lexicographic preferences. These bundles too have a rational number r2 lying between the interval u (y1,0) and u(y1,1). This implies r2>r1. But this can't hold as we don't have one to one correspondence between real numbers and rational numbers. That's why we don't have a utility function that can represent lexicographic preferences.

Rahul Sunny answered 1 year ago

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