Keynesian model functions In The Keynesian economy,
I have the following model

Here, the production function $F(N,K) = Y/K = A(N/K)^{1.10}$ and by the labor demand function $F_N(K,N)= N/K= b_0(w/p)^{b_1}$.
right?
That is, what is the F(K,N)=? and $F_N(N,K)=?$
Here , I mean that $F_N(N,K)$ is marginal product of labor.
To get back to the original production function just multiply both sides with capital. Here:
$$Y/K = A (N/K)^{1.1} = F(N/K,1) \implies Y = AN^{1.1}K^{-0.1}  =F(N,K)$$
Also, the marginal product of labor here will be:
$$F_N'(N,K) =  1.1 A N^{0.1}K^{-0.1} = 1.1 A (N/K)^{0.1}$$