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Question
If the demand function is D = 150 - p2 - 3p, find marginal revenue, average revenue and elasticity of demand for price p = 3.
Solution
Demand function D = 150 -p2 - 3p
∴ Revenue = D × P
R = 150p - p3 - 3p2
∴ Marginal revenue Rm = `(dR)/(dP)`
Rm = 150 - 3p2- 6p
where p = 3
Rm = 150 - 3(32) - 6(3)
Rm = 105
Average revenue RA = `R/P`
RA = 150 - p2 - 3p
When p = 3
RA = 150-32 -3(3)
∴ RA = 132
Elasticity of demand
η = `(-p)/D xx (dD)/(dp)`
= `(-p)/(150 - p^2 - 3p) xx (-2p - 3)`
= `(-3)/(150 - 3^2 - 3(3)) xx (-2(3) - 3)`
= `27/132`
= `9/44`
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