2. (54 points) Short-run costs. Suppose w = 1, r = 10 and K = 20.
a) (5 points) We have $TC = w \left(\frac{1}{k}\right) q^3 + rK = \left(\frac{1}{20}\right) q^3 + 200$
On one graph (with q on the horizontal axis), graph the Total Cost, Variable
Cost, and Fixed Cost functions.
Pay attention to the shape of the curves, where they intercept the axes and each
other (if they do), and the position of the curves relative to each other.
b) (9 points) Using the graph from part a, show how AC, AVC, and MC can be shown
when q = 20.
c) (5 points) From the TC function in part a, find
Marginal Cost, Average Cost, and Average Variable Cost.