# How can I show whether the following function is Increasing, Decreasing, or Constant returns to scale? [closed]

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!

## 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

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.