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## In Problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand function p2 + 2p + q = 49 at p =

Question

In Problem, p is in dollars and q is the number of units.

(a) Find the elasticity of the demand function

p2 + 2p + q = 49 at p = 6.

(b) How will a price increase affect total revenue?

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Mathematics
5 months
2021-08-30T06:44:29+00:00
2021-08-30T06:44:29+00:00 1 Answers
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## Answers ( )

Answer:

-14

Explanation:

Elasticity of demand is the degree of change in demand after a change I’m price, basically demand’s sensitivity to price change.

Formula for calculating price elasticity is: change in price/change in quantity =dq/dp

Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:

2p+2+dq/dp=0

dq/dp=-2p-2

Given p =6, we substitute:

dq/dp=-2×6-2

dq/dp=-12-2

dq/dp=-14

With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.