Question

If the demand function is D = 150 - p² - 3p, find marginal revenue, average revenue and elasticity of demand for price p = 3. 

Answer 1

 Demand function D = 150 -p² - 3p 

∴ Revenue = D × P

R = 150p - p³ - 3p²

∴ Marginal revenue R_m = `(dR)/(dP)`

R_m = 150 - 3p²- 6p 

where p = 3

R_m = 150 - 3(3²) - 6(3) 

R_{m =} 105

Average revenue R_A = `R/P`

R_A = 150 - p² - 3p 

When p = 3

R_A = 150-3² -3(3) 

∴ R_A = 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`