Both nations with high and low standard of living face the problem of scarcity because the human wants and needs are unlimited while the resources are limited. Scarcity refers to an opportunity cost, in which it doesn’t matter how high the standard of living every person cannot have everything that they desire as long as resources are limited. If you want something more, you have to let something go. It's nothing to do with the level of living standard. A million dollar in lottery will not be the best way to escape this issue as scarcity focus on the giving up one thing to get something else.