Question

et cred 1. Word Sign in References Mailings Review View Help Tell me what you want to do S Shani Optimization Questions 1. You've been hired by Nielsen Company to study the market for potatoes. Demand in the potato market is characterized by the demand function QQdd 25-12 PP. Where Pis the market price of a potato and Odd is the quantity of potatoes demanded. The marginal revenue of the fifth potato produced is The demand function is Q = 25 1/2 P 1 Delive the inverse demand function (Solve the demand function for P) 2 Derive the revenue equation R=PXQtake the night-hand side of the inverse demand equation (which equals P) and multiply it by Q 3. Take the derivative of R with respect to Q in calculus terms, marginal revenue (MR) - R/09 Once you have the derivative, put in a value of 5 for Q. You then have the marginal revenue of the 5th unit As a different approach to the question, start with Q-4 and put into the inverse demand equation. Then solve for P. The total revenue for 4 units would then be P x 4 Then use Q-5 and put into the inverse demand equation Solve for P (A different price is required to sell 5 units rather than 4) Take the new price and multiply it by 5 to get the total revenue for 5 units Using this approach, the marginal revenue of the 5th unit would be the increase in total revenue between the 4th unit and the 5th unit. What is now your answer for the marginal revenue? is your answer the same as you got by using the calculus approach? Why or why not? ferdinand, thanks for using Pro Referral! Which pro tackled your p.. ackspace

I need some help with this.

Answer 1

Solution -

Given demand function is Q= 25-1/2P

Going by the procedure given in the question we will find out the marginal revenue.

1) Inverse demand function shows prices as a function of quantity demanded. Inverse demand function is

P=f(Qd)

0 bo 8= 25-2 Inverse Demand Punction: - 9 - 25-Ź P - P = 25-0 P= 2(25-8) í P=50-20 Diverse Demand function. Revenue Equation : - PXQ P = 50-20 So, Revenue (50-29) - 508-29² So, Revenue Equation will be & R=508-282 calculus terms, we have 8 MR= d.RS

MR= d(508-202) do MR = 50 - 40. So, At 8 = 5, we will get marginal revenue of the fifth potato MR = 50-40 - 50-485 = 50-20 I MR = 30

Total revenue is the total money income generated by the sale of goods. The revenue will be (R)=P×Q

Marginal revenue is the addition to the total revenue by the sale of an extra unit of good.

By other method we will get

10:41 Inverse Demand equation. P = 50- 20 s At 8=4. P=50-2x4 = 50-8=42 So, Revenue = PXQ =PX4 = 42 X 4 = 168 Also, At 8=5. p=50-2x5 = 50-10 = 40 [Q=5] Revenue = PxQ = 4085 0 = 200

from us Subtracting MR= 200- 168 MR = 32

Yes the marginal revenue calculated by two approaches are different.

​​​​​​We always use calculas method to calculate marginal revenue because it takes into consideration of both change in total revenue and change in total quantity. As in other approach, the total has no deltas as it measures directly the total sales, but it fails to incorporate the link between change in sales and change in quantity. So the answer by both the methods is slightly different.