knowledge assignment

Knowledge Assessment 1 (PRACTICE)
NAME: ________________________________________________________________________
Situation: Your CFO drops by your desk and says that she wants you to prepare some notes for her on the following sensitive situation. Your company is going to be introducing new value-added app and service for smartphones. The app and service have been testing marketed in two areas with the following results: when the price is $260 the estimated quantity sales were 1.2 million but when the price was $175 the estimated quality sales were 3.0 million.
Listing the data series needed to solve this problem using marginal analysis
We will need the following data series to be able to apply the marginal analysis concept. a) Quantity of product sold, b) respective prices, c) respective marginal costs, and d) respective marginal Revenues
List the calculations would you do to find the “optimal” price?
The following are the necessary calculations needed to solve for optimal price (Dyer & Proll, 1977)
Step1: Calculate the marginal cost function
Step2: Calculate the associated marginal revenue function
Step3: For optimal price set the two functions to be equal (set MC=MR)
Step4: Solve for the optimal price P in the equation
Using the two data points for price and quantity calculate the formula for this company’s demand curve (i.e. (a) and (b) for the formula P = a –b (Q)).
Q = a + b (P)
b = (Q2-Q1) / (P2-P1)
= (3-1.2) / (175-260)
= -1.8/85
Therefore Q = a -1.8/85P.

Plug in P=175 and Q = 3M in the equation to get a = 6.705
Q = 6.705-0.02P, therefore P=6.705/0.02-Q/0.02, i.e P = 316.625-47.22Q
a = 316.625 b = 47.22
The demand curve
Q = 316.625 + 47.22P

Reference
Dyer, M. E., & Proll, L. G. (1977). Note—On the Validity of Marginal Analysis for Allocating Servers in M/M/c Queues. Management Science, 23(9), 1019-1022.