Transcript 12 gb

Mathematics for Business Decisions, part II
Project 1:
Marketing Computer Drives
Math 115b
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Goal
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.
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Definitions
 Market: A market is people or organizations
with purchasing power and willingness and
authority to buy
 Product: Good or service bought and sold
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Pricing Situations
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Pricing Situations
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Where do we fit?
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
The functions
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Demand Function, D(q)
 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?
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Demand Curve
 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 qaxis.
Demand Curve, D(q)
Unit price, D(q)
(in $)
Total quantity (q)
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Revenue Function, R(q)
 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,
R(q)  q  D(q)
 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?
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Revenue Curve
 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, R(q)
Total
Revenue
(in $)
Quantity (q)
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Cost Function, C(q)
 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?
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Cost Curve
 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, C(q)
Total cost
(in $)
Quantity (q)
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Profit Function, P(q)
 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?
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Profit Curve
Profit Curve, P(q)
Total profit
(in $)
Quantity (q)
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Class Project: Card Tech, Inc.
 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
Ekstrom
will be an assumption for our project
Math 115b
Project 1: Marketing Computer Drives
From the Goals
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?
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Research
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Information Given to You
 In Marketing Data.xls, you have the results from the test
markets (also shown here):
Test Markets
Ekstrom
Market
Number
Market
Size
Price
Projected Yearly
Sales
(number of drives)
1
2
3
4
5
6
144,900
4,627,600
1,049,800
2,946,500
5,042,300
3,617,600
$265.95
$276.95
$287.95
$299.95
$310.95
$321.95
570
17,178
3,801
9,941
15,594
10,859
Math 115b
Project 1: Marketing Computer Drives
Information Given to You
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Questions to Answer
 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:





Ekstrom
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
Math 115b
Project 1: Marketing Computer Drives
Additional Questions to be
Answered in Project
 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?
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Team Projects
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Preliminary Report
 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
Ekstrom
Math 115b
Project 1: Marketing Computer Drives
Preliminary Report
 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?
Ekstrom
Math 115b