I am trying to construct a differentiable, concave function $f(x,y)$ where $f : \mathbb{R}^2 \to \mathbb{R}$ (but the domain I'll mainly be focussing on is $\mathbb{R}^2_{\geq 0}$) that satisfies $f_x < 0$ and $f_y > 0$.
Query $1:$ What could be a possible construction?
Query $2:$ Which of the following figures below is the correct representation of the level curves of the function?
