Suppose we have a production function with constant returns to scale. Let us denote it by $F(A,K,L)$ where $A$ is the technology, $K$ the capital and $L$ Labor. Further assume the first partial derivative of $L,K$ are both positive and the second partial negative. How to show the production function is concave in $K$ and $L$ but not strictly so?
This problem is from Acemoglu's Intro to Modern Economic Growth. I don't quite understand what it means to say the function is concave in $K$ and $L$. Do I need to show that $F(K,L)$ (treating A as constant) is concave? or do I show $F(K)$ and $F(L)$ are concave (treating L,A or K,A as constants)?
If it is the latter, it seems the problem seems trivial by the second derivative test.