Question

The weekly sales of Honolulu Red Oranges is given by q = 896 − 20p.(A) Calculate the price elasticity of demand when the price is $32 per orange (yes, $32 per orange†). = __________(B) The demand is going ___(Up or down?)____ by ______% per 1% increase in price at that price level.(C) Also, calculate the price that gives a maximum weekly revenue. $_______.(D) Find this maximum revenue. $________.

Answer 1

Answer with Step-by-step explanation:

Since we have given that

q = 896-20p

p = $32

.(A) Calculate the price elasticity of demand

As we know that

$e=-\dfrac{dq}{dp}\times \dfrac{p}{q}\\\\e=-(-20)\times \dfrac{32}{896-20p}\\\\e=\dfrac{20\times 32}{896-20p}\\\\e=\dfrac{640}{896-20p}\\\\e=\dfrac{640}{896-640}\\\\e=\dfrac{640}{256}=2.5$

(B) The demand is going down with increase in 15 increase in price at that price level, as we know that there is inverse relationship between price and quantity demanded.

(C)  Also, calculate the price that gives a maximum weekly revenue.

$R=pq\\\\R=p(896-20p)\\\\R=896p-20p^2$

We first find the first derivative:

$R'(p)=896-400p$

So, it becomes,

$896-40p=0\\\\40p=896\\\\p=\dfrac{896}{40}=\ 22.4$

R=-40<0, so, it will give maximum revenue.

(D) Find this maximum revenue.

Maximum revenue would be $R=pq\\\\R=22.4(896-20\times 22.4)\\\\R=\ 10035.2$