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www.facebook.com/o t like&notif; id-1492318206287776 Take a Test-Carissa Cox Google Chrome Secure https//www.mat aspx?tes 153306458&centerwin; yes hxi.com/Student/PlayerTest JFCSW: Bartley MAT 170-5701 Spring 2017 Test: Test 3 This Question: 1 pt 9 of 18 (7 complete) v For the following demand function, find a. E, and b. the values of q (f any) at which total revenue is maximized q 39.800 7p? a. Determine the elasticity of demand. E Type an expression using p as the variable) b. Determine the value of q that maximizes the revenue Select the comect choice below and if necessary in the answor box within your ch A. Total revenue is maximized at about q 26532 (Round to the nearest whole number as needed) O B. No values of q maximize total revenue. I. (ru) More Click no select your answer(s) a 9

Explanation / Answer

The given demand function is q = 39800 - 7p^2

a) Elasticity, E of a demand function is calculated using the following formula:

E = (dq/dp)*(p/q)

In our case, dq/dp = -14p

So, E = (dq/dp)*(p/q)

= -14p*{p / (39800 -7p^2)}

E = -14p^2 / (39800 - 7p^2)

We will assume E to be positive since as we are considering the absolute value of the price elasticity of demand.

b) To find the value of q at which the revenue is maximum, the price elasticity E of demand should be 1 or unitary.

Therefore, for E = 1, we get

14p^2 / (39800 - 7p^2) = 1
14p^2 = 39800 - 7p^2

21p^2 = 39800

or p^2 = 39800/21

Now substituting above value of p^2 into the given demand function to get the value of q which gives maximum revenue, we get

q = 39800 – 7 * 39800/21
= 39800 – 39800/3
= 39800 * 2/3
= 26533.3333
= 26534 units (rounded off to next whole number) ……. ANS

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