For the demand function q equals Upper D (p) equals 346 minus p , find the following. a) The elasticity b) The elasticity at pequals89 , stating whether the demand is elastic, inelastic or has unit elasticity c) The value (s) of p for which total revenue is a maximum (assume that p is in dollars)

Question

Mathematics

Hensley

29 November, 00:34

For the demand function q equals Upper D (p) equals 346 minus p , find the following. a) The elasticity b) The elasticity at pequals89 , stating whether the demand is elastic, inelastic or has unit elasticity c) The value (s) of p for which total revenue is a maximum (assume that p is in dollars)

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Julie · Answer 1

a. Ped = - p / q

b. Ped at p = 89 : 0.35 (Inelastic Demand)

c. Total Revenue maximising price = 173

Step-by-step explanation:

a. Price Elasticity of Demand is responsiveness in demand due to price change. Ped = [∂q / ∂p] x [p / q]

Demand Function Given : q = 346 - p

Derivating q with respect to p : ∂q / ∂p = - 1

Putting value of ∂q / ∂p in Formula:

P Ed = - 1 x p / q

Price Elasticity of demand = - p / q

b. Elasticity at p = 89

Putting p value in elasticity, q value from demand function:

= 89 / (346-89) = 89 / 257

= 0.35

Since Price Elasticity of Demand < 1, Demand is Inelastic.

c. Total Revenue is maximum when demand is unitary elastic, price elasticity of demand = 1

Ped = - p / q = 1

Putting value of q : - p / (346 - p) = 1

- p = 346 - p → p + p = 346

2p = 346 → p = 173