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)

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):Marketing Data.xls Information Given to You

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