Solve the problem.
-A beverage company works out a demand function for its sale of soda and finds it to be where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic?

Question

Solve the problem.
-A beverage company works out a demand function for its sale of soda and finds it to be Solve the problem. -A beverage company works out a demand function for its sale of soda and finds it to be where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic? A) For p < 69 cents B) For p > 30,450 cents C) For p > 276 cents D) For p < 138 cents

Solve the problem. -A beverage company works out a demand function for its sale of soda and finds it to be where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic? A) For p < 69 cents B) For p > 30,450 cents C) For p > 276 cents D) For p < 138 cents

where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic?

Quizplus · Accepted Answer

For the demand to be inelastic, the absolute value of the elasticity of demand must be less than 1. So we need to find at what prices the absolute value of the derivative of the demand function (which gives the elasticity of demand) is less than 1. Taking the derivative of the demand function gives:

d/dx (11ebb6d7_48c3_afa6_b437_afc5f81fdc91_TB8593_11) = -0.0000012x + 0.0000672

To find when the elasticity of demand is inelastic, we want to find the prices where the absolute value of this derivative is less than 1:

|-0.0000012x + 0.0000672| < 1

Simplifying:

-1 < -0.0000012x + 0.0000672 < 1

Subtracting 0.0000672 from all three parts of the inequality:

-1 - 0.0000672 < -0.0000012x < 1 - 0.0000672

Simplifying:

-1.0000672 < -0.0000012x < 0.9999328

Dividing by -0.0000012 (and reversing the inequalities since we are dividing by a negative number):

138.7 < x < 83330.7

So the elasticity of demand is inelastic for any quantity of sodas sold less than 138 or greater than 83330. In terms of prices, since p is measured in cents, prices less than 69 cents (when x = 138) and greater than 416,653 cents (when x = 83330) result in inelastic demand. The only answer choice that includes a price less than 69 cents is A.

Solve the Problem. -A Beverage Company Works Out a Demand Function for Its