How can I show whether the following function is Increasing, Decreasing, or Constant returns to scale? 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!
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.