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\noindent 21-121 \hfill Fall 2000

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{\bf Assignment 4 Supplementary Problems}
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In Problems 1 - 3, find the marginal cost and the marginal revenue for
the given average cost functions and demand equations.

\begin{enumerate}
\item $\overline{c} = {\displaystyle \frac{10}{q}} + 5 + e^{-.1q}$

$p = 100 e^{-.01q}$

\item $\overline{c} = {\displaystyle \frac{100}{q} + \frac{50}{\sqrt{q}}} + 2$

$p= {\displaystyle \frac{100}{\sqrt{q}}}$

\item $\overline{c} = {\displaystyle \frac{500}{q}} + .01q + 10$

$p={\displaystyle \frac{100}{q+1}}$

\item Suppose that the demand for a monopolist's product is given
by\newline $p = {\displaystyle \frac{200}{q+1}}$, where $p$ is the price
per unit and $q$ is the number of units, and that the average cost
function is given by $\overline{c} = 2 + {\displaystyle \frac{50}{q}}$.

\begin{enumerate}
\item[(a)] Find an expression for the profit $P$ as a function of $q$.

\item[(b)]  Find all values of $q$ at which ${\displaystyle
\frac{dP}{dq}} = 0$.
\end{enumerate}

\end{enumerate}

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