Small farmers are sometimes price takers, i.e. the price of wheat is set in the global market. Suppose a small farm produces soybeans that sell at a market price of $6 a bushel. In addition, the farmer understands her cost structure for production; her total cost for producing "q" bushels is given by:
TC = .1q^2+ 2q + 100
a. Does this farm has increasing returns to scale, constant returns to scale, or decreasing returns to scale? describe how you can tell.
b. Find the profit-maximizing choice of q for this small farm, and find out the profits that will be earned at this choice of q.
c. Draw a graph illustrating this situation and labeling the choice of q.