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October 11, 2018\\
{\Large {\bf Notes on the Shutdown Decision }}
\noindent
{\sc 1. Teaching the Decision to Shut Down if $P 6\\
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The marginal cost is V-shaped, and its minimum is 4, at $Q = 6$. Its minimum is lower than AVC's because it doesn't average in all of the high values of marginal cost for $Q<6$.
Note that the marginal cost jumps at 6, from MC=4 to MC = 16. There is a kink in the total cost curve at $Q=6$, so the slope suddenly increases.
What is the optimal output for the firm? That depends on the market price. If the price is zero, the firm should produce $Q=0$, for profits of -49. It has to pay the fixed cost of 49, but the marginal cost is 16 at $Q=0$, so it isn't worth producing anything. Clearly, if $P<4$, the firm should produce $Q=0$.
How about if the price rises to $P=4$? Then we could use the rule of picking $Q$ so $MC(Q)=P$. Doing that, we'd have $MC=16-2Q = 4$, so $12=2Q$, and $Q=6$. But this would be a very bad idea, because $P