The demand function for a certain make of exercise bicycle sold exclusively through cable television is , where p is the unit price in hundreds of dollars and x is the quantity demanded/week.
Compute the elasticity of demand and determine the range of prices corresponding to inelastic, unitary, and elastic demand.

Question

The demand function for a certain make of exercise bicycle sold exclusively through cable television is  , where p is the unit price in hundreds of dollars and x is the quantity demanded/week. ​
Compute the elasticity of demand and determine the range of prices corresponding to inelastic, unitary, and elastic demand.
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Quizplus · Accepted Answer

To determine the elasticity of demand, we use the formula: E = (dp/p) / (dx/x) where E is the elasticity of demand, p is the price, x is the quantity demanded, and dp/dx means the change in p or x over a given time period. Differentiating the demand function with respect to p, we get: dx/dp = -651/11p^2 Substituting this into the formula for elasticity, we get: E = (dp/p) / (-651/11p^2 * p/x) E = (-11/651) * p/x E = -0.0169p/x We can see that the elasticity of demand is negative, which means that as the price increases, the quantity demanded decreases. To determine the range of prices corresponding to inelastic, unitary, and elastic demand, we need to look at the absolute value of E: - If |E| < 1, demand is inelastic (i.e. a change in price has a relatively small effect on the quantity demanded). - If |E| = 1, demand is unitary (i.e. a change in price has a proportional effect on the quantity demanded). - If |E| > 1, demand is elastic (i.e. a change in price has a relatively large effect on the quantity demanded). Substituting the demand function into the formula for E, we get: |E| = 0.0169p/x - Inelastic demand: |E| < 1 0.0169p/x < 1 p/x < 59.17 p < 59.17x - Unitary demand: |E| = 1 0.0169p/x = 1 p/x = 59.17 p = 59.17x - Elastic demand: |E| > 1 0.0169p/x > 1 p/x > 59.17 p > 59.17x Therefore, the range of prices corresponding to inelastic, unitary, and elastic demand is: inelastic: p < 59.17x unitary: p = 59.17x elastic: p > 59.17x Based on this, the correct answer is B, where the elasticity of demand is 11eb651f_cb70_2cf3_b0a1_8148cb94ef54_TB8255_11.

The Demand Function for a Certain Make of Exercise Bicycle