Question

Consider the price-demand equation given by p= 8/5 – x/2.500 Calculate E(0.25), where E is the elasticity of demand, and select the correct interpretations of the result.

A. When p = 0.25 an increase in price will result in increased revenue.
B. When p = 0.25 the elasticity of demand satisfies E(0.25) < 1, which is inelastic.
C. When p = 0.25 the elasticity of demand satisfies E(0.25) < 1, which is elastic.
D. When p = 0.25 an increase in price will result in decreased revenue.

Answer 1

When p = 0.25 for the price-demand equation p = 8/5 - x/2500, the elasticity of demand is calculated to be -0.185, indicating inelastic demand. Therefore, an increase in price will result in decreased revenue, and the correct interpretations of the result are options B and D.

Step-by-step explanation:

To calculate the elasticity of demand E(0.25) for the price-demand equation p = 8/5 - x/2500, we first need to find the quantity demanded (x) when p = 0.25:

0.25 = 8/5 - x/2500

Now, we solve for x:

• 0.25 = 1.6 - x/2500
• x/2500 = 1.6 - 0.25
• x/2500 = 1.35
• x = 1.35 * 2500
• x = 3375

We've found that the quantity demanded is 3375 units when p = 0.25. Next, we calculate the elasticity using the formula for price elasticity of demand:

E(p) = (p/Q) * (dQ/dp)

Where p is the price, Q is the quantity demanded, and dQ/dp is the derivative of the quantity demanded for price. Since our quantity demanded equation is x = 2500* (8/5 - p), to find dQ/dp we differentiate the equation concerning p, yielding dQ/dp = -2500. Substituting in the values we have:

E(0.25) = (0.25/3375) * (-2500)

E(0.25) ≈ -0.185

The value of E(0.25) is less than 1 in magnitude, which indicates inelastic demand. Therefore, selection B is correct: When p = 0.25 the elasticity of demand satisfies E(0.25) < 1, which is inelastic. This implies that a price increase will lead to a decrease in the total revenue, hence option D is also correct. As a result, options A and C are incorrect interpretations.