1
$\begingroup$

enter image description here

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

$\endgroup$
1
$\begingroup$

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 $L$, you`re 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 input`s 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.

| improve this answer | |
$\endgroup$
1
$\begingroup$

The dotted line is just to help you read the scale and compare the isoquantas at each production level. It touches all the isoquantas at the point where you have equal inputs of labour and capital.

The rest of the explanation is on the figure itself - it's just an example of increasing / constant / decreasing returns to scale.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.