Question

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)

Answer 1

a. Ped = - p /q

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

c. Total Revenue maximising price = 173

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