I have a max utility function, therefore; U(x,y)= max(2x,y) and I am trying to find the demand function x = x(𝑝x , 𝑝y , 𝑀), note this function cannot be differentiated. I am familiar that the utility function states that it is best to have x=0 and all of the good y, or vice versa. So I've been trying to solve with the budget line making one x=0 and then again y=0 but I am unsure what to do from this point?

Working so far: p1x+p2y=M when y=0 x=m/p1

& when x=0 y=m/p2

From this point, I am lost? Thanks in advance

I have a max utility function, therefore; U(x,y)= max(2x,y) and I am trying to find the demand function x = x(𝑝x , 𝑝y , 𝑀), note this function cannot be differentiated. I am familiar that the utility function states that it is best to have x=0 and all of the good y, or vice versa. So I've been trying to solve with the budget line making one x=0 and then again y=0 but I am unsure what to do from this point?

Working so far: p1x+p2y=M when y=0 x=m/p1 U= 2m/p1

& when x=0 y=m/p2 U= m/p2

So now I have two equations in terms of U