Transcript Deman, Revenue, Cost, and Profit Functions

Demand, Revenue, Cost,
and Profit Functions
Math 174, Spring
2004
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
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How should you do this?
Units of Demand Function
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Will use two variables (not used in
text)–
qu is the quantity in single units
 qk is the quantity in thousand units
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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
Units of Demand Function
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We have the following proportion:
Test Market Sales
National Sales (in K's)
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Size of Test Market Size of National Market (in K's)
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 K’s)
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Round answers to nearest whole unit
Demand Curve
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Once you have the national sales (in K’s)
for each test market -
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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
Revenue Function
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Revenue, R(qk), is given in millions of dollars
for selling qk thousand units
So, R(qk) = D(qk)*qk *1000
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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
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So, our formula should be
R(qk)=(D(qk)*qk)/1000
Revenue Curve
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You need to use the data you generated
for your demand curve and determine
what the corresponding values are for
your revenue function
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Use R(qk) function determined on previous
slide
When you graph your revenue data, you
will have quantity (in K’s) along x-axis
and total revenue (in M’s) along y-axis
Cost Function
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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
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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
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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
Variable Cost
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To determine the variable cost, you will
need to use the marginal cost of
production
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For example, if you produce 1,200 drives:
• The first 500 thousand cost $115 per drive
• (500*1000*115)/1,000,000 =
(500*115)/1000=$57.5 million
• The next 600 thousand cost $100 per drive
• (600*100)/1000 = $60 million
• The rest cost $90 per drive
• (100*90)/1000 = $9 million
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The sum of the results give the final variable
cost of $126.5 million
COST function
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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
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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
Total Cost
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Regardless of how you calculate the total cost,
you will need to understand each step
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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
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Why should you graph both curves together?
Cost graph is quantity (K’s) vs. Total Cost (M’s)
Profit
Since the total cost and the total
revenue is in millions, profit will also
be in millions
 Profit Curve will be quantity (K’s) vs.
total profit (M’s)
 Create a curve for profit by
subtracting total revenue and total
cost
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What should you do?
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Start a new Excel file, generate the data for your
information
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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
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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