economics maths task help: Co XYZ has established that the relationship between...

[amkarchampionov]

Hi Folks,
Some help needed to resolve following task:




Co XYZ has established that the relationship between the quantity demanded for one of its products and the price it charges is given by the following function:


q = 750 - 5p


Where q is the quantity demanded per week and p is the price charged.


(a) What price should be charged if the business wishes to maximize total revenue?






(b) What quantity will the firm sell per week when it is maximizing total revenue?


(c) What will be the value of total revenue when it is being maximized?


(d) What quantity will the firm sell if it charges a price of 100?


(e) What is the price elasticity of demand when price is 100?


Any help appreciated
Thanks.

 

[ksdhart2]

Co XYZ has established that the relationship between the quantity demanded for one of its products and the price it charges is given by the following function:

q = 750 - 5p

Where q is the quantity demanded per week and p is the price charged.

What have you tried? Where are you getting stuck? Please share with us all of your work, even if you know it's wrong. If you're stuck at the very beginning and don't even know where to start, here's a few hints to hopefully get you thinking in the right direction.

(a) What price should be charged if the business wishes to maximize total revenue?

How does your textbook/professor define "total revenue?" You're given a formula for quantity, in terms of price, so what then would be the formula for total revenue? If you've taken calculus before, what happens if you use the standard method of setting the derivative equal to 0? If you haven't, what method(s) has your class used to maximize functions? How far do you get in applying those method(s)?

(b) What quantity will the firm sell per week when it is maximizing total revenue?

In part (a), you found the price that maximizes revenue. Using the given formula for quantity, what result do you get?

(c) What will be the value of total revenue when it is being maximized?

In part (a) you found the price that maximizes revenue. In part (b) you found the resulting quantity. What then is the maximum revenue?

(d) What quantity will the firm sell if it charges a price of 100?

You're given a formula for quantity, in terms of price. So, what happens if you plug in a price of 100 into that formula?

(e) What is the price elasticity of demand when price is 100?

How does your textbook/professor define "price elasticity of demand?" Were you, perhaps, given a formula for this? How far have you gotten in applying that formula?