# Question on returns of scale in isoquants What does the dotted line in the diagram show and what are they called?

I am also wondering why the steepness of the isoquants changes at Q=3 for the third diagram.

Thanks

I've computed this in WolframAlpha and I think it'll help you understand just what exactly a production function is. Remember, the production function $Y=f(K,L)$ is defined by $f:\mathbb{R}^2 \to \mathbb{R}$. When you see a graph with axis in $K$ and $L$, youre seeing a part of a 3D object, the surface that a function with domain in $\mathbb{R}^2$ generates. The isoquants are just contour lines of it.
The change in the isoquant's steepness is a consequence of the shape a Cobb-Douglas Produtcion Function's surface. The non-linear nature of Cobb-Douglas model makes its contour lines change steepness as $f(K,L)$ gets bigger, as production goes up. There's an interesting economic intuition behind it. The more inputs a firm employs in its production process, the smaller the marginal rate of technical substitution of the optimal plant is because of diminishing marginal returns. As a firm employs more of an input, the smaller is that inputs marginal productvity. As a firms employs more and more of two inputs, capital and labor, both the marginal productivity of capital and labor get smaller, meaning a smaller marginal rate of technical substitution.