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)

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

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: