Question

The marginal revenue function on sales of q units of a product is R'(q)=240-18√q dollars per unit.

Estimate the total revenue if sales are 100 units.
What is the marginal revenue at 100 units?
Estimate the total revenue if sales are 101 units.

Answer 1

I'm not very familiar with economics or its terminology. Is the idea of the marginal revenue function simply that it gives the revenue per unit for a given number of units sold?

Answer 2

Why is it listed as R'(q) instead of just R(q)?

Answer 3

R(q) would be total revenue and R'(q) is revenue/ unit?

Answer 4

R'(q) I believe would be the derivative. And usually.

Answer 5

the revenue has to do with cost but I don't think it'd be per unit.

Answer 6

Usually that is what ' indications, but I don't see how that makes any sense in this case.

Answer 7

but I'm not sure:/

Answer 8

Be a darling and look in your book to find out for me?

Answer 9

okay, one sec.

Answer 10

Revenue is price times quantity. The vertical distance between revenue and cost functions equals profit.

Answer 11

Makes sense. That's good.

Answer 12

Okay, so the way I'm reading this then is that that function gives you the revenue PER UNIT for a given number of units. So if you want to know your total revenue, you need to multiply the output of that function by the number of units produced.

Answer 13

the output of the original function times the 100?

Answer 14

Yes. To get the total revenue.

Answer 15

Oh my. I believe I read that wrong. It's like you thought. It's written as R'(q) because it gives the CHANGE in revenue.

Answer 16

the change?but then how would i calculate the output and then calculate separately for the 100?

Answer 17

Okay, so R'(100) means that whatever you sold at first, now you're selling 100 more. And the output of the function gives you (change in revenue/change in number of units)

Answer 18

Reading from wikipedia, by the way.

Answer 19

Make sense?

Answer 20

I just don't understand how I'd be getting the output of the function with the 100 being plugged in.

Answer 21

Not sure what your question is.

Answer 22

so to get the revenue of sales at 100, I'd plug in 100 into the function?but then how would I get the marginal revenue?

Answer 23

Plugging in 100 into the equation would give you the change in revenue from 0 units sold to 100 units sold, except it's divided by 100 to give increase in revenue per unit.

Answer 24

and that would give me the revenue of sales at 100?

Answer 25

If you multiplied it by 100 it would.

Answer 26

but if that's how you get the revenue?how would you get the marginal? sorry to be asking so many questions!

Answer 27

The marginal is the original output of the function. You multiply it by total units to get the total revenue.

Answer 28

but how do I know what units to multiply by?

Answer 29

So if you put some number into that equation, say n, you'll get the revenue increase per unit for n units. If you want the total revenue increase for n units then, you multiply by n.

Answer 30

okay so this is the deal basically: to get the revenue, I plug in 100, then divide the function by 100, the multiply by 100? and to get the marginal, I just plug in 100?

Answer 31

R'(100) = marginal revenue at 100 units.
R'(100) * 100 = total revenue at 100 units.

Answer 32

oh oh oh! I think I get it:) and then for the estimate of 101, I plug in 101 and multiply that by 101 for the total revenue at 101?

Answer 33

Yes.

Answer 34

so I entered the values, and the total revenue was double of what I got.

Answer 35

should I try that for the following problems?

Answer 36

It looks similar to last problem