Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Ekstrom Math 115b Mathematics for Business Decisions, part IIProject 1:Marketing Computer DrivesMath 115bEkstrom Math 115b Project 1: Marketing Computer DrivesYour 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. GoalEkstrom 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 DefinitionsEkstrom 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 SituationsEkstrom 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 SituationsEkstrom 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 functionsEkstrom 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 CurveUnit 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 CurveQuantity (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 CurveQuantity (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