Ekstrom Math 115b Mathematics for Business Decisions, part II Project 1: Marketing Computer Drives...
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Transcript of Ekstrom Math 115b Mathematics for Business Decisions, part II Project 1: Marketing Computer Drives...
Ekstrom Math 115b
Mathematics for Business Decisions, part II
Project 1:Marketing Computer Drives
Math 115b
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Your goal is three-fold: To find the price of a particular product that
will maximize profits. Determine the number of units that will be
sold at the optimal price. Determine the maximum profit that is
expected from the sales of your particular product.
Goal
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Market: A market is people or organizations with purchasing power and willingness and authority to buy
Product: Good or service bought and sold
Definitions
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Perfect Competitor: The amount sold does not affect the product’s price firms produce identical commodities sold to
consumers who are identical from the point of view of producers
The producer can sell as much as it likes at the market price
in theory, perfect competition generates the perfect price
Pricing Situations
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Monopoly: The amount of the product that is sold affects the product’s price In fact, this is the only thing that affects the
product’s price The product price is set by the seller/producer The producer has market power
Pricing Situations
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Our company has temporary monopoly power for our product for three years.
This means that we have a new product that does not have an exact competitor
Where do we fit?
Ekstrom Math 115b
Project 1: Marketing Computer Drives
To achieve the goals of the project, we will need to look at different mathematical functions Recall: What is the definition of a function?
We have 4 functions in particular that we will need to study Demand, Cost, Revenue, and Profit
Note: You will need to be extremely careful with the units on each of the axes for all of the functions
The functions
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Gives the unit price, D(q), at which a company can charge in relation to the total quantity (q) of the product that it sells at that price
The demand curve, which is the graph of D(q), is generally downward sloping in a monopoly setting (generally horizontal in perfect competition)
Why?
Demand Function, D(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
We can look at the curve and see at what unit price we can sell a specified number of items When the unit price is high, the total quantity we sell is low When the unit price is low, the total quantity we sell is high For our purposes we are going to assume that the
maximum quantity that can be sold is where the curve intersects the q-axis.
Demand Curve
Unit price, D(q)
(in $)
Total quantity (q)
Demand Curve, D(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
To determine the total revenue you will receive from selling a product, you multiply the total number of goods sold by the unit price of the goods Revenue,
What happens if you sell a small amount for a high price?
What happens if you sell a large amount for a low price?
What does the curve look like?
Revenue Function, R(q)
)()( qDqqR
Ekstrom Math 115b
Project 1: Marketing Computer Drives
We can look at the total revenue that is produced when a specified number of items is sold
Our graph starts out low, gets high, and then goes low again
Revenue Curve
Quantity (q)
Total Revenue (in $)
Revenue Curve, R(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
When you are making goods, you will incur costs
There are two types: Fixed Costs: Incurred even if units are not
produced Variable Costs: Unit-based production
Examples: labor, lighting, etc.
What does the curve look like?
Cost Function, C(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
We can look at the total costs that are incurred when a particular number of goods are produced The more goods that are produced, the higher the
total cost
Cost Curve
Quantity (q)
Total cost (in $)
Cost Curve, C(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Q: When does a company make a profit? A: When the revenue exceeds the costs Thus, the profit function is total revenue minus total
cost or P(q) = R(q) – C(q). What happens when the difference is positive? When
will this happen? What happens when the difference is negative?
When will this happen? How does this translate to a graph?
Profit Function, P(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Profit Curve
Quantity (q)
Total profit (in $)
Profit Curve, P(q)
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Card Tech developed and patented a new type of computer drive, the 12-GB Features the ability to store 12 gigabytes of information on
a rewritable credit card sized wafer Under the conditions of the patent, Card Tech has the
exclusive right to produce and market the new technology during the next three years, giving them temporary monopolistic power*.
* This will be an assumption for our project
Class Project: Card Tech, Inc.
Ekstrom Math 115b
Project 1: Marketing Computer Drives
1. How should they price the 12-GB such that it will produce a maximum profit during the coming year?
2. How many drives can they expect to sell at that price?
3. How much profit might they realize from sales at that price?
From the Goals
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Card Tech’s marketing department did research on potential buyers Estimates that there are 350 million potential customers in
the national market during the coming year Studied 6 test markets to determine the fraction of the
potential buyers who would actually buy the 12-GB at various price levels
Assumption #2: From past experience, they will assume that the 12-GB will have a quadratic demand function
Research
Ekstrom Math 115b
Project 1: Marketing Computer Drives
In Marketing Data.xls, you have the results from the test markets (also shown here):
Information Given to You
Market Number
Market Size
PriceProjected Yearly
Sales (number of drives)
1 144,900 $265.95 5702 4,627,600 $276.95 17,1783 1,049,800 $287.95 3,8014 2,946,500 $299.95 9,9415 5,042,300 $310.95 15,5946 3,617,600 $321.95 10,859
Test Markets
Ekstrom Math 115b
Project 1: Marketing Computer Drives
You also know the costs of production – both fixed and variable
For the class project, you are given the following: Fixed overhead costs of $135,000,000 ($135 million) during the
coming year Variable costs:
First 800k drives -- $160 per drive Next 400k drives -- $128 per drive Rest of the drives -- $72 per drive
Note the units on the values given – will be very important in the project
Information Given to You
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Using the information that is given, Card Tech wants to analyze the pricing and production of the product, the 12-GB. They want to know: a price in order for them to achieve maximum profit how many they will sell at the optimal price the maximum profit expected how sensitive the profit is to changes in optimal quantity what the consumer surplus will be if the profit is
maximized
Questions to Answer
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Additionally, Card Tech wants to know the following: What profit can they expect if the unit price of the drive is
$299.99? How much should they pay for advertising if the campaign
increases demand for the drives by 10% at all price levels? How would the 10% increase in demand affect the optimal
price? Would it be smart if they put $15M into training and
streamlining if it reduces the variable production costs by 7% for the coming year?
Additional Questions to be Answered in Project
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Go online and get the team data (in an Excel file) under D2L Content, “Project 1” and “Team data” It contains test market data, trend line directions,
and production cost estimates Also, it has 9 questions that will need to be
answered at the end of the project
Assume that your company has temporary monopolistic power for the next 3 years
Team Projects
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Everyone will go on the same day – order of presentation will be random
Casual dress (no shorts, wrinkled shirts, sleeveless shirts, low cut or short shirts/skirts, flip-flops) – if you have to ask, don’t wear it!
Each team will present for 5 minutes Bring a hard copy of your slides for me
(handout – 6 slides per page) Attach a team project signature page to your handout, signed
by all contributing members Be prepared for computer mishaps – have backup or hard copy
of slides
Preliminary Report
Ekstrom Math 115b
Project 1: Marketing Computer Drives
Introduce your company and your job descriptions (your choice – be creative)
Come up with a unique product that makes sense with the prices given Remember product differentiation
Know basic terms and assumptions Do not give list of definitions but work into presentation
Present the data Give an initial guess for the max profit
How?
Preliminary Report