Elasticity and price

Question

Suppose the demand for a product is given by D(p)=-3p+139

A) Calculate the elasticity of demand at a price of $25. (Give your answer to three decimal places.)

Elasticity =

B) At what price do you have unit elasticity? (Round your answer to the nearest penny.)

Price =

Answer 1

D(p) = -3x +139 = q

elasticity = dq/do x p/q

dq/dp = -3

p/q = 25/(139-75) = 25/64 when p=25

elasticity = -3 x 25/64 = -75/64 = about-1.172

but by convention they take the absolute value so

elasticity = 1.172 rounded to 3 decimals

unit elasticity means = 1 (or -1)

-3 x p/(139-3p) = -1

3p/(139-3p) = 1

3p = 139 -3p

6p = 139

p = 23 1/6 for unit elasticity

= 23.167 rounded to 3 decimals

had the sign been + in D(p)

quantity demanded = 3p + 139 This is absurd, as it says consumers buy more when the price rises. That's true only in the rare case of a "Giffen good" major example is demand for potatoes during the potato famine in Ireland

elasticity of demand = dq/dp/q/p = pdq/qdp

dq/dp = 3

when p =25, q = 3(25) + 139

then elasticity = 25/214 x 3 = 75/214 =about 0.35047

= 0.350 rounded to 3 decimals

unit elasticity = 1

= 3 x p/q = 3 x p/(3p+139) = 1, solve for p

cross multiply

3p +139 = 3p

139 = 0 which is impossible. elasticity of demand is never = 1

but set 3p/(3p+139) = -1 then

3p = -3p -139

6p = -139

p = -139/6 = - 23 1/6 which is also impossible unless the government is subsidizing purchases. but generally lower bound on price is zero