Indifference curves
Plotting Utility functions
Suppose the a utility function, \(U(x,y)=xy\), where \(x\) is the quantity of good \(x\), and, \(y\) is the quantity of good \(y\). Since the utility depends on two variables, \(x\) and \(y\), if we draw a graph of \(U\) it requires \(3\) dimensions.
Indifference curves
Since drawing in 3d is hard it is useful to consider indifference curves. These are contor lines of the utility function. The intereactive diagram below shows the utility function plotted in 3d, with some indifference curves above. The curves show all the \(x\), \(y\) points which have the same utility, hence the consumer is indifferent to the combination of \(x\) and \(y\) shown by the line.
Download the surface as an stl. You can 3d print the stl and feel the resource for yourself.
See the coordinates that make the surface here.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 1 | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 |
| 2 | 0.0 | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 | 12.0 | 14.0 | 16.0 | 18.0 | 20.0 |
| 3 | 0.0 | 3.0 | 6.0 | 9.0 | 12.0 | 15.0 | 18.0 | 21.0 | 24.0 | 27.0 | 30.0 |
| 4 | 0.0 | 4.0 | 8.0 | 12.0 | 16.0 | 20.0 | 24.0 | 28.0 | 32.0 | 36.0 | 40.0 |
| 5 | 0.0 | 5.0 | 10.0 | 15.0 | 20.0 | 25.0 | 30.0 | 35.0 | 40.0 | 45.0 | 50.0 |
| 6 | 0.0 | 6.0 | 12.0 | 18.0 | 24.0 | 30.0 | 36.0 | 42.0 | 48.0 | 54.0 | 60.0 |
| 7 | 0.0 | 7.0 | 14.0 | 21.0 | 28.0 | 35.0 | 42.0 | 49.0 | 56.0 | 63.0 | 70.0 |
| 8 | 0.0 | 8.0 | 16.0 | 24.0 | 32.0 | 40.0 | 48.0 | 56.0 | 64.0 | 72.0 | 80.0 |
| 9 | 0.0 | 9.0 | 18.0 | 27.0 | 36.0 | 45.0 | 54.0 | 63.0 | 72.0 | 81.0 | 90.0 |
| 10 | 0.0 | 10.0 | 20.0 | 30.0 | 40.0 | 50.0 | 60.0 | 70.0 | 80.0 | 90.0 | 100.0 |
The corresponding indifferent curve for \(U(x,y)= c\), where \(c\) is a constant, is plotted below. Move the slider to change the value of \(c\). It starts with \(c=5\).