What is the price elasticity?? p=50, q=50e^(-0.02)?
- Thread starter mikaelaw
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The price elasticity of demand is defined as:
\(\displaystyle \displaystyle E_d\equiv\frac{p}{q}\cdot\frac{dq}{dp}\)
You are given \(\displaystyle p=50\).
Now, your quantity demanded \(\displaystyle q\) should be a function of price \(\displaystyle p\), but seems to be a constant instead. Are you certain you have given the correct expression for quantity demanded?
\(\displaystyle \displaystyle E_d\equiv\frac{p}{q}\cdot\frac{dq}{dp}\)
You are given \(\displaystyle p=50\).
Now, your quantity demanded \(\displaystyle q\) should be a function of price \(\displaystyle p\), but seems to be a constant instead. Are you certain you have given the correct expression for quantity demanded?
D
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I'm not too sure, I have had 5 attempts but they have all been wrong, I was really hoping somebody could explain to me step by step how to solve this problem.
Please show us in detail - at least one of your wrong attempts.
Okay, so for one of my attempts, I differentiated the p/q equation:
[(50e^(-0.02p)(1)-(p)(50e^(-0.02p))(-0.02)]/(50e^(-0.02p))^2
with that, I got 1.
To find \(\displaystyle \dfrac{dq}{dp}\) you differentiate \(\displaystyle q = e^{(-0.02p)} = e^u \implies \dfrac{dq}{du} = e^u\ and\ \dfrac{du}{dp} = -0.02.\)
\(\displaystyle So \dfrac{dq}{dp} = \dfrac{du}{dp} * \dfrac{dq}{du} = -0.02e^{(-0.02p)}\)
So what does \(\displaystyle \dfrac{p}{q}\) equal? So what does \(\displaystyle \left|\dfrac{p}{q} * \dfrac{dq}{dp}\right|\) equal?
You now have a general expression in p. So if p = 50, then what?