Question

what should the indifference curve between income and crime look like?

Answer 1

First thing we have to note that, while income is an economic good (everyone wants more of and more income implies more utility). On the other hand crime is an economic bad (everyone wants less of it and more crime implies more disutility).

Now, we know that indifference curves are representation of utility function that maintains constant utility i.e in other words along a indifference curve utility have to be fixed at a particular level.

With this knowledge we can easily draw the indifference curve between income and crime as following-

Here we are measuring Crime along the horizontal axis and measuring Income along the vertical axis.

Suppose intially the society is consuming at point A, where he consumes C1 units of Crime and I1 Units of crime and thus enjoying a fixed level of utility given by point A.

Now, if the society moves from point A to Point B, here at point B the society is consuming more of Crime and same income as of Point A. As we know that more crime implies more disutility, we can say that the society is worse off at point B than in point A i.e. the utility level at point B is lower at point B than point A.

Hence to keep the utility level fixed at amount given by point A we have to provide more of Income to the society which is now at point B. By moving from B to C will provide the society more income and thus more positive utility. This gained positive utility by moving from B to C will compensate the disutility gained from moving point A to point B.

Thus point A and Point C are indifferent i.e. this two budle provide same level of utility. Hence joining A and C will provide us the indifference curve between income and crime.