Consider the statemen
A manufacturer of aluminum doors is currently selling 500 doors per week at a price of \$85 each. If the price were lowered to \$80 each, an additional 70 doors per week could be sold.
I wanna find the current elasticity of demand for the doors, and also estimate the current value of the manufacturer's marginal-revenue function.
To estimate the current elasticity of demand for the aluminum doors, we can use the midpoint formula. We will consider the original quantity ($Q1$) of $500$ doors at a price $P1$ of $ \$85 $ and $Q2$ of $570$ doors at price $P2$ of $ \$80 $, if we consider the formula, then
$$Ed=\frac{\frac{Q2-Q1}{\frac{Q2+Q1}{2}}}{\frac{P2-P1}{\frac{P2+P1}{2}}}=\frac{\frac{570-500}{\frac{570+500}{2}}}{\frac{80-85}{\frac{80+85}{2}}}=-\frac{231}{107}=-2.158$$
For the second part, maybe i can use the following
$$Mr=\frac{\delta TR}{\delta Q}=\frac{(\$ 80 - \$ 85)*500+(\$ 80 \cdot 70)}{70} \approx 44.28$$
Can this work?