这是一份manchester曼切斯特大学ECON31002T作业代写的成功案例

This relation is a completely general specification of marginal revenue, which, if $P$ is factored out from the right-hand side, can be rewritten as
$$
M R=P\left(1+\frac{Q}{P} \times \frac{d P}{d Q}\right)
$$
Note that the term $Q / P \times d P / d Q$ in the preceding expression is the reciprocal of the definition for point price elasticity, $\epsilon_{p}=d Q / d P \times(P / Q)$ :
$$
\frac{Q}{P} \times \frac{d P}{d Q}=\frac{1}{\frac{d Q}{d P} \times \frac{P}{Q}}=\frac{1}{\epsilon_{p}}
$$
Thus, marginal revenue can be rewritten as
$$
M R=P\left(1+\frac{1}{\epsilon_{p}}\right)
$$

ECON31002T COURSE NOTES ：

$$
M C=M R
$$
and, therefore,
$$
M C=P\left(1+\frac{1}{\epsilon_{p}}\right)
$$
which implies that the optimal or profit-maximizing price, $P^{}$, equals $$ P^{}=\frac{M C}{\left(1+\frac{1}{\epsilon_{p}}\right)}
$$