Demand, Revenue, Cost, and Profit Functions - PowerPoint PPT Presentation

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Demand, Revenue, Cost, and Profit Functions

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qu is the quantity in single units. qk is the quantity in thousand units ... We are going to define Marginal Cost to be the price, in dollars per item, for ... – PowerPoint PPT presentation

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Title: Demand, Revenue, Cost, and Profit Functions


1
Demand, Revenue, Cost, and Profit Functions
  • Math 174, Spring 2004

2
Demand Function
  • D(q) is the unit price at which q units of a
    product can be sold
  • Experience suggest a quadratic demand function
  • For your data, you will need to come up with a
    function based on test market data
  • How should you do this?

3
Units of Demand Function
  • Will use two variables (not used in text)
  • qu is the quantity in single units
  • qk is the quantity in thousand units
  • Test market data must be scaled up to the
    national level
  • At national level, demand is presented as the
    unit price at which qk thousand drives can be
    sold

4
Units of Demand Function
  • We have the following proportion
  • Note The size of your national market (in your
    data) is given in millions. You will have to
    rewrite this number in thousands so the units are
    correct.
  • You can then solve the proportion for the
    national sales (in Ks)
  • Round answers to nearest whole unit

5
Demand Curve
  • Once you have the national sales (in Ks) for
    each test market --
  • Plot the points (qk vs. unit price)
  • Fit a trend line to the data
  • Show equation (make sure all coefficients go out
    to 8 decimal places)
  • Use equation to determine points for demand curve
    need a lot of points
  • Use points to plot a smooth demand curve

6
Revenue Function
  • Revenue, R(qk), is given in millions of dollars
    for selling qk thousand units
  • So, R(qk) D(qk)qk 1000
  • This answer is in millions
  • For example, if D(qk)119.95 and qk 893, then
    R(qk)107,115,350
  • We want the unit to be millions and also the
    answer to be a smaller number (so we can work
    with it easier)
  • We can divide our answer by 1,000,000 to get
    about 107 million dollars
  • So, our formula should be R(qk)(D(qk)qk)/1000

7
Revenue Curve
  • You need to use the data you generated for your
    demand curve and determine what the corresponding
    values are for your revenue function
  • Use R(qk) function determined on previous slide
  • When you graph your revenue data, you will have
    quantity (in Ks) along x-axis and total revenue
    (in Ms) along y-axis

8
Cost Function
  • If your total revenue is in millions of dollars,
    then your total cost must be also
  • Total cost is the fixed cost plus the variable
    cost
  • Fixed cost is in millions of dollars need to
    rewrite it so the unit is millions
  • Example 21,600,000 is rewritten as 21.6 million
  • You need to determine the variable cost for each
    amount of product you are producing
  • We are going to define Marginal Cost to be the
    price, in dollars per item, for production at a
    given number of items

9
Variable Cost
  • To determine the variable cost, you will need to
    use the marginal cost of production
  • For example, if you produce 1,200 drives
  • The first 500 thousand cost 115 per drive
  • (5001000115)/1,000,000 (500115)/100057.5
    million
  • The next 600 thousand cost 100 per drive
  • (600100)/1000 60 million
  • The rest cost 90 per drive
  • (10090)/1000 9 million
  • The sum of the results give the final variable
    cost of 126.5 million

10
COST function
  • To determine the total cost, you can add the
    fixed cost and the variable cost
  • To do this for every quantity, it would be
    tedious to determine a formula
  • Can use COST function located under USER DEFINED
    formulas built in
  • If you are generating your data and graphs in a
    new Excel workbook, you will need to copy the
    COST module over from Marketing Focus.xls
  • Follow directions in slides 58-60 in Notebook or
    on CD

11
Total Cost
  • Regardless of how you calculate the total cost,
    you will need to understand each step
  • Using the COST function make sure you
    understand why you are entering what you are for
    each of the arguments in the dialog box
  • You should have a column that has the total cost
    for each particular quantity
  • Once you have the data, you should create a graph
    that illustrates the cost display both the
    revenue and cost on one set of axes
  • Why should you graph both curves together?
  • Cost graph is quantity (Ks) vs. Total Cost (Ms)

12
Profit
  • Since the total cost and the total revenue is in
    millions, profit will also be in millions
  • Profit Curve will be quantity (Ks) vs. total
    profit (Ms)
  • Create a curve for profit by subtracting total
    revenue and total cost

13
What should you do?
  • Start a new Excel file, generate the data for
    your information
  • Do not forget to copy the COST module
  • Create each one of the curves talked about
    demand, revenue, cost, and profit
  • Work with the same units and coefficient
    precision as is in the Class Project
  • I will be solving each of your projects and will
    assume the same accuracy as the on-line text
  • Your information should match mine at the end of
    the project
  • Do not put this off! Your work will pile up if
    you leave too long
  • It will also be a part of the next homework
    assignment
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