<p>This is just assumption on the model.</p>
<p>There are some functions for which you can mathematically say they always have constant returns to scale.</p>
<p>For example, if <span class="math-container">$F(K,L)=AK^{0.5}L^{0.5}$</span> then we know it will always have constant returns to scale since when you increase both factors <span class="math-container">$K$</span> or <span class="math-container">$L$</span> by some scalar <span class="math-container">$z$</span> output also increases by <span class="math-container">$z$</span>.</p>
<p><span class="math-container">$$ F(zK,zL) = A(zK)^{0.5}(zK)^{0.5}=z AK^{0.5}L^{0.5} = zF(K,L)$$</span></p>
<p>So from the above we know that this (Cobb-Douglas) function always have constant returns to scale.</p>
<p>There is a large number of functions that have this property. Usually papers want to be general so they will just assume constant returns of scale without saying what the function is.</p>

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2022-09-25T19:21:21.290Z
2022-09-25T19:21:21.290Z
1muflon1
<p>This may be a stupid questions as I am just studying undergrad economics honours but how do we know that the solow model has diminishing returns to its input and harrod-domar has constant returns to its inputs from the definitions of the models? Like for example if in the harrod domar model, we take Y to be a function that has diminishing returns to scale then how can we say that it always has CRS?</p>

<solow><model>
How do we know Solow has DRS and Harrod-Domar has CRS from the definitions of the models?
viktor nikiforov
# How do we know Solow has DRS and Harrod-Domar has CRS from the definitions of the models?

(Asked by: username_0 on 2022-09-25)

This may be a stupid questions as I am just studying undergrad economics honours but how do we know that the solow model has diminishing returns to its input and harrod-domar has constant returns to its inputs from the definitions of the models? Like for example if in the harrod domar model, we take Y to be a function that has diminishing returns to scale then how can we say that it always has CRS?

**Tags:** solow, model

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## 1 answers

### Answer by username_1 on 2022-09-25. Score: 1 | Accepted answer

This is just assumption on the model.

There are some functions for which you can mathematically say they always have constant returns to scale.

For example, if $F(K,L)=AK^{0.5}L^{0.5}$ then we know it will always have constant returns to scale since when you increase both factors $K$ or $L$ by some scalar $z$ output also increases by $z$.

$$ F(zK,zL) = A(zK)^{0.5}(zK)^{0.5}=z AK^{0.5}L^{0.5} = zF(K,L)$$

So from the above we know that this (Cobb-Douglas) function always have constant returns to scale.

There is a large number of functions that have this property. Usually papers want to be general so they will just assume constant returns of scale without saying what the function is.


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