Question 23 of 26intermediate🔧 ApplyNumerical3 marks

Consider the demand curve D(p)=10−3pD(p) = 10 - 3p. What is the elasticity at price 53\frac{5}{3}?

Correct Answer

The price elasticity of demand at price p = 5/3 is -1 (unitary elastic).

Step 1: Identify the demand function parameters The demand curve is given as D(p) = 10 - 3p, which can be written as q = 10 - 3p. This is of the form q = a - bp, where a = 10 and b = 3.

Step 2: Calculate quantity demanded at price p = 5/3 Substituting p = 5/3 in the demand function: q = 10 - 3 × (5/3) q = 10 - 5 q = 5

Step 3: Apply the elasticity formula From the context, the formula for price elasticity of demand for a linear demand curve is: e_D = -b × (p/q)

Substituting the values: e_D = -3 × (5/3) / 5 e_D = -3 × (5/3) × (1/5) e_D = -5/5 e_D = -1

Therefore, the elasticity at price 5/3 is -1, indicating unitary elastic demand.

Exercise: EXERCISES | Q: 23
For More Understanding

Explanation

This question tests the student's understanding of calculating price elasticity of demand for a linear demand curve. The context provides the formula e_D = -b(p/q) for a linear demand curve q = a - bp. Students need to first identify the parameters a and b from the demand function, then calculate the quantity demanded at the given price, and finally substitute all values in the elasticity formula. The answer -1 indicates unitary elastic demand, which occurs at the midpoint of a linear demand curve.

Solution Steps

  1. Step 1: Identify parameters from demand function q = 10 - 3p: a = 10, b = 3

  2. Step 2: Calculate quantity at p = 5/3: q = 10 - 3(5/3) = 10 - 5 = 5

  3. Step 3: Apply formula e_D = -b(p/q) = -3(5/3)/5 = -1

PreviousNext