<p>You have <span class="math-container">$$F(x_1,x_2)=x_2\sin\bigg(\frac{x_1}{x_2}-\pi\bigg).$$</span>
If you multiply all factors by <span class="math-container">$t$</span> you get
<span class="math-container">$$F(tx_1,tx_2)=t x_2\sin\bigg(\frac{tx_1}{tx_2}-\pi\bigg).$$</span>
Simplify the fraction and you are almost done.</p>

CC BY-SA 4.0
2018-11-17T12:00:38.763Z
2018-11-17T12:00:38.763Z
Michael Greinecker
<p>in the case of for example a production function, returns to scale mean the effect when all factors of production are multiplied by a certain constant, with what constant is the production level multiplied?
i) the same constant as the factors of production (constant returns to scale)
ii) a larger constant (increasing returns to scale)
iii) a smaller constant (decreasing returns to scale)
So the right approach is to simply fill in a constant (let's call it c) in your function.
cX2(sin((cX1/cX2)-pi)
and try to rewrite it to 
d(X2(sin((X1/X2)-pi))
where d is the constant with which y is multiplied as a consequence of multiplying X1 and X2 with c</p>

CC BY-SA 4.0
2018-11-17T11:58:25.340Z
2018-11-17T11:58:25.340Z
user18214
<p>I need to show whether or not the following function is increasing, decreasing, or constant returns to scale, but I can't figure out how to extract the <em>t</em> from it when it is put in the form <span class="math-container">$y(tX_1, tX_2)$</span>.
<span class="math-container">$$
y = X_2\sin{\left(\frac{X_1}{X_2}-\pi \right)}
$$</span>
Is there any other way of showing IRS, DRS, and CRS? Any help would be appreciated!</p>

<microeconomics>
How can I show whether the following function is Increasing, Decreasing, or Constant returns to scale?
Amna Ul Haq
# How can I show whether the following function is Increasing, Decreasing, or Constant returns to scale?

(Asked by: username_0 on 2018-11-17)

I need to show whether or not the following function is increasing, decreasing, or constant returns to scale, but I can't figure out how to extract the *t* from it when it is put in the form $y(tX\_1, tX\_2)$.
$$
y = X\_2\sin{\left(\frac{X\_1}{X\_2}-\pi \right)}
$$
Is there any other way of showing IRS, DRS, and CRS? Any help would be appreciated!

**Tags:** microeconomics

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## 2 answers

### Answer by username_1 on 2018-11-17. Score: 3

You have $$F(x\_1,x\_2)=x\_2\sin\bigg(\frac{x\_1}{x\_2}-\pi\bigg).$$
If you multiply all factors by $t$ you get
$$F(tx\_1,tx\_2)=t x\_2\sin\bigg(\frac{tx\_1}{tx\_2}-\pi\bigg).$$
Simplify the fraction and you are almost done.


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### Answer by username_2 on 2018-11-17. Score: 0

in the case of for example a production function, returns to scale mean the effect when all factors of production are multiplied by a certain constant, with what constant is the production level multiplied?
i) the same constant as the factors of production (constant returns to scale)
ii) a larger constant (increasing returns to scale)
iii) a smaller constant (decreasing returns to scale)
So the right approach is to simply fill in a constant (let's call it c) in your function.
cX2(sin((cX1/cX2)-pi)
and try to rewrite it to
d(X2(sin((X1/X2)-pi))
where d is the constant with which y is multiplied as a consequence of multiplying X1 and X2 with c


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