Final answer:
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.