Assume that the production function for the removal of atmospheric carbon is as follows:

Q= MN - 0.8M² - 0.2N², where M= human-made capital and N- natural capital.

a) Re-write the production funstion given a level of human-made capital of 10 units. Find its maximum point. Then, find the average natural capital productivity (AP_N). Find where the AP_N reaches maximum.

b) Find the marginal productivity of natural capital (MP_N). At what value N is MP_N zero?

c) Graph the production function and label of its maximum point of output. On a separate graph, draw the MP_N and the AP_N functions as functions of natural capital. Lavel point (Value of N) for which AP_N is at its maximum.