0
$\begingroup$

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!

$\endgroup$

closed as off-topic by Giskard, Herr K., Jamzy, Kitsune Cavalry Nov 23 '18 at 16:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – Giskard, Herr K., Jamzy, Kitsune Cavalry

3
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

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

$\endgroup$

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