Graphing indifference curves to visualize solutions?
I am having trouble with being able to graph indifference curves. This is a particularly important skill to have especially when trying to visualize corner solutions, and when the Lagrangian method doesn’t necessarily give us the solution i.e. perfect substitutes.
I particularly struggle when the Utility function in question has a mixture of different types of curves.
For example:
$ U(x, y) = min $ { $ x, y $ } + $ max $ { $ \frac{x}{2}, \frac{y}{2} $ }, or
$ U(x, y) = min $ { $ ax + by, cx + dy $ }
My approach for the first one: I individually plotted the two curves by setting them equal to a constant. I got a L shaped curve for the min part after evaluating various cases (x = y, x > y, x < y), and the opposite of that for the max part again after evaluating cases.
However, I am having a hard time visualizing the combination of both. Like how would the shifts effect the shape? In general, what strategy do you recommend when trying to plot different types of indifference curves such as ones mentioned above?
You can easily plot these using Desmos.
On the left side, define the utility function with the equation
[Math Processing Error]$$ U\left(x,y\right)=\min\left(x,y\right)+\max\left(\frac{x}{2},\frac{y}{2}\right) $$ Then ask for the set of points $ (x,y) $ which satisfy the equation for a utility level, e.g. 2, $$ 2 = U\left(x,y\right). $$ It is important to place the function on the left hand side when defining the function (first equation), and to place the function on the right hand side when asking for the set of points (second equation). Here is the implementation.