For the following demand function find a E and b the values

For the following demand function, find a. E, and b. the values of q (If any) at which total revenue is maximized 4 40,200 a. Devermine the elasticity of demand, E (Type an expression using p as the variable.) b, Determno the value of qthat maximizes the revenue. Select O A Total revenue is maximized at about q ?B. Novales of q maximize total revenue. correct choice below, and if necessary, inthe answer box within your choice. Round to the nearest whole number as needed.) Click to select your answens). Tom:%2018 2728088,%203.%20\"%20falsel.\" 28 MacBook Pro 5 6 8

Solution

q = 40,200 - 8p²

a. Elasticity of demand, E = (dq/dp)*(P/q)

From the demand equation we get, (dq/dp) = d(40,200 - 8p²)/dp = - 16 p

Therefore, E = -16p (p/q) = -16p²/q = -16p²/(40,200 - 8p²)

Answer: E = -16p² / (40,200 - 8p²)

B) Total revenue is maximized when value of elasticity is (-1) or, when absolute value of elasticity is 1 i.e. Total revenue is maximized when the demand is unitary elastic.

Therefore,

- 1 = - [16p²/(40,200 - 8p²)]

Or, 16p² = 40200 - 8p²

Or, 24p² = 40200

Or, p² = 1675

From the demand equation we get, when p²= 1675,

q = 40200 - (8*1675) = 26800

Therefore, total revenue is maximized at q = 26800