Question

If the cost function and demand curve for certain product are C(x) = 60x + 7200 and p = 300 – 2x respectively.
Find
Total revenue function

Answer 1

Isn't revenue the product of the cost function and demand curve?

Answer 2

^that's what i was thinking, but it's not based on any proof... just kinda made sense.

Answer 3

the cost function doesn't affect the total revenue. TR=x*p(x).

Answer 4

TR=price*quantity

Answer 5

if you want to find the profit though, just subtract C(x) from TR.

Answer 6

Never took an economics class and I am trying to figure out what is what?

Is x the number of units of the product?
Is C(x) the cost to purchase or to produce?

Answer 7

And p(x) means?

Answer 8

x is the number of units of the product. C(x) is the cost to produce.

Answer 9

p(x) is the price charged for x units

Answer 10

*for each of the x units being sold

Answer 11

Okay, in that case revenue = x * p(x) makes sense.
So for this problem we don't really need C(x) since they don't ask for profit.

Answer 12

revenue function????

Answer 13

Revenue function = x * p(x) = x * (300 – 2x) = 300x - 2x^2

Answer 14

Thanks

Answer 15

I looked up the definition of a demand curve: it is a curve drawn with price per unit of the product along the y axis and the quantity demanded on the x axis. As the demand increases the price per product will decrease as is evidenced by the negative slope of 300 - 2x. So it makes sense to multiply x and p(x) to get the total revenue function.

Answer 16

That seems odd... doesn't high demand allow for higher price per unit? low demand should dictate low cost per unit

Answer 17

When things are produced in small numbers, there is a lot of overhead involved and the company has to charge a lot more per unit to cover the production cost and make some profit. As the demand increases, the price charged per unit will decrease. But overall they will make a lot more profit because they are selling a lot more.

We can see that in real cases. Whenever a new product is introduced it costs a lot. Then as it becomes popular the price goes down.

Answer 18

If the cost function and demand curve for certain product are C(x) = 60x + 7200 and p = 300 – 2x respectively.
Find
Total revenue function
P(x)=R(x)-C(x)
Where P(x)=profit, R(x)=Revenue (R(x)=xp, where p is the price C(x)=cost (a+m(x)), m(x)=margin cost

P(x)=R(x)-C(x)
P(x)=(x(300 – 2x))-(60x + 7200)
P(x)=300x – 2x^2-60x -7200

Profit equation will be:
P(x)=-2x^2+240x-7200

Revenue rquation
R(x)=xp
R(x)=x(300 – 2x)
R(x)=300x-2x^2

Cost equation which you gave me.
C(x)=60x + 7200

Answer 19

High demand and low supply then the price will be higher
High demand and high supply the price will be lower.