Integration Applications: Economists who study production of goods by a firm con

Question

Integration Applications:

Economists who study production of goods by a firm consider two functions. The revenue function R(x) is the revenue the firm receives when x number of units are sold. The cost function C(x) is the cost the firm incurs when producing x number of units. The derivatives of these functions R (x) and C (x) are called by economists the marginal revenue and cost function. What does integral_1000^5000 R (x) dx represent? The increase in revenue when production is increased from 0 units to 5000 units. The increase in revenue when production is increased by 1000 units. The increase in revenue when production is increased by 5000 units. The increase in revenue when production is increased from 1000 units to 5000 units.

Explanation / Answer

R ' (x) is the marginal revenue function

When we integrate R ' (x) from 0 to x, it means the total revenue obtained when selling the firxt 'x' products

When we integrate R'(x) from 'a' to 'b', it means the same as integrating from (0 to b) and subtracting that from the integral of (0 to a)

Integral from 0 to b is the total revenue generated in selling the first 'b' products

Integral from 0 to a is the total revenue generated in selling the first 'a' products

So, when we subtract, we get the INCREASE in revenue when we sell 'b' instead of 'a' products

So, this is the increase in revenue when production is increased from 1000 to 5000 units

Option D -----> ANSWER

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.