Problem
Take a production function of only labor, L, with the following form
??(??)={??2?????√ for ??∈[0,1) for ??∈[1,2]f(L)={L2 for L∈[0,1)L for L∈[1,2]
A. Define this production function in Python
B. Write a function to calculate the marginal product of labor (MPL) numerically by using a method similar to what we did in class.
C. Consider the scenario where you increase the scale of production by a factor of 10 percent more labor. Calculate the returns to scale for a grid on ??∈[0,1.5]L∈[0,1.5]. (Hint: For this, you may need to write your own version of the returns_to_scale function specific to this production function.)