Let TC = 100 + 150Q - 12Q2 + 2Q3.) Find the equations for MC and AVC.

Let TC = 100 + 150Q - 12Q2 + 2Q3.

a.) Find the equations for MC and AVC.

b.) Calculate the Q' that minimizes MC (when slope of MC = 0) and the Q" that

minimizes AVC (when slope of AVC = 0 and when AVC = MC).

c.) Calculate MC and AVC at their minima. Draw MC and AVC with Q' and Q", and

solving for MC and AVC at Q = 0.

d.) Under what price will a firm shut-down in the short-run?

e.) All firms maximize profits at the Q where MR = MC. And for a firm in a

competitive market, P = MR. Assuming competition here, solve for equilibrium Q if

P = 150. At that level of Q, calculate AFC, AVC, ATC, FC, VC, TC, TR, and

profits/losses. Shut down or operate? Why?

f.) At P = 180, profit-maxing equilibrium output is 5. (You can take that on faith—or

can you figure out how one would determine that?) Again, calculate AFC, AVC,

ATC, FC, VC, TC, TR, and profits/losses.

g.) Draw two new-and-improved versions of your graph, illustrating profits/losses for

Q = 4 and Q = 5.