How do you draw indifference curves given a utility function?

Question

how? and how do you know if its a convex set or not?

Answer 1

Hold U constant

Solve the equation for q2 in terms of q1 (so that you get an equation that looks something like q2=U[something]q1

Pick values for U to graph specific indifference curves.

Graph it like you would any (x,y) function.

If it's a convex set, the curves will be bowed towards the origin.

Answer 2

Let us take the utility function U= U(x , y). where U stands for utility and x and y are two goods.

Now this is a general form of the utility function. You will be given a specific function like U= 4(x+y) + 1/(x+y)

What you do is as follows:

Take U= 4.25 and find out the different sets values of x and y for which U=4.25. This sets of values give different points on the indifference curve with Utility equal to 4.25. You can see

if x= 1 and y= 3, U=4.25.

Again, if x= 2, y=2, U=4.25

Again if x= 3, y= 1, U =4.25.

Or, x =0, y=4, U=4.25

So, you plot the points (1,3),(2,2), (3,1), (0,4) and (4,0) and join them and you get one indifference curve.

To get another indifference curve with higher utility, you can set U=8.50 and find out the values combination of (x,Y) to get the points in the new indifference curve.