Question

The relationship d = 5000 − 25p describes what happens to demand (d) as price (p) varies. Here, price can vary between $10 and $50

Consider prices of $20, $30, and $40. Which of these three price alternative will maximize total revenue?

Answer 1

To maximize total revenue using the demand equation d = 5000 - 25p, we calculate total revenue at prices $20, $30, and $40. The calculations show that the price of $40 maximizes total revenue, with a total of $160,000.

Step-by-step explanation:

The relationship d = 5000 − 25p describes the demand (d) based on the price (p).

To determine which price ($20, $30, $40) maximizes total revenue, we need to evaluate the total revenue (TR) at each price level.

Total revenue is calculated as TR = price × demand.

• At $20: $20 × (5000 − 25(20)) = $20 × 4500 = $90,000
• At $30: $30 × (5000 − 25(30)) = $30 × 4250 = $127,500
• At $40: $40 × (5000 − 25(40)) = $40 × 4000 = $160,000

Comparing these total revenues, the price of $40 yields the highest total revenue.

Therefore, pricing the good at $40 will maximize total revenue.