Indifference curves- a general question?

Question

how do you check whether 2 bundles are on the same indifference curve when you know the utility function?

ex: u(x1, x2) = 4(x1)^.5 +x2

1st bundle: x1 = 16 units of nuts, x2 = 20 units of berries

2nd bundle: x1= 64 units of nuts, x2 = 80 units of berries

3rd bundle: x1 = 12 units of nuts, x2 = 20 units of berries

Answer 1

plug in the quantity of nuts and berries for each bundle:

If the number you get for each bundle is equal then they are on the same IC

Answer 2

Good question. An indifference curve is an isometric curve - meaning that all points on that line have the same utility value given by a utility function.

Think of it as a graph in cartesian space (x and y axes). If you take a simple line, say y=x, then you know that the points (1,1), (7.8, 7.8), (-1, -1) are all on that line.

Same thing here - test your bundles by plugging x1 and x2 into the parametric equation u(x1, x2) and see what the utility level is. Where they are equal, you have points on the same utility curve. Where they are not equal, you have different utility curves mapped out.

This kind of problem is just plug-n-chug.