Question

Are preferences with the following utility function representation u(x, y) = min[x, y] complete, transitive, and continuous?

Answer 1

this type of utility function shows the perfect complement goods. the prefernce is more is better none of the complete transtive or continuous.

Suppose that we are looking at our shoe example so our utility function is U = min(L, R) where L = left shoe and R = right shoe. Recall, that our values for utility do not matter as long as they display the following characteristic:

More is better, so having 2 left shoes and 2 right shoes is better than having 1 left shoe and 1 right shoe, which we can see is true since:

min(2,2) = 2 - which is the utility from having 2 left and right shoes

min(1,1) = 1 - which is the utility from having 1 left and 1 right shoe

So this characteristic is satisfied.