STRAIGHT LINE MODELS

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STRAIGHT LINE MODELS

• DEMAND
• SUPPLY
• EQUILIBRIUM Point
• EXAMPLES
• EXCEL's Goal Seek
• Straight Line DEPRECIATION 1.25

M160-L05 1.2b
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DEMAND
If suppliers (in the aggregate) produce xp units
of a commodity, the demand equation gives the
price they must accept to sell it all. Suppliers
would like a very high price, but they will have
to lower it somewhat to encourage enough buying.
Hence the demand curve decreases with an increas
of the number of units produced. A straight line
demand equation gives the price as demand p
po m x where po is the price to sell none
of the commodity, and m is the (negative)
slope, showing how fast the price must decrease
as the suppliers produce more.
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SUPPLY
Assuming consumers (in the aggregate) want to buy
(consume) xc units of a commodity, the supply
equation gives the price they must pay to buy a
given quantity xc. Consumers would like a very
small price, but they will have to pay a higher
price to persuade supplies to sell. Hence the
supply curve increases as the number of units
increases. A straight line supply equation gives
the price as supply p po m x where
po is the price to buy none of the commodity, po
is near zero, and m is the (positive) slope,
showing how fast the price increases as the
consumers buy more.
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EQUILIBRIUM POINT
If the producers produce more than consumers want
to consume, then some of the commodity is stored
as inventory. But if the producers produce less
than consumers want to consume, then some of the
commodity is removed from storage, and
inventories are decreased. When the quantity
consumed exactly equals the commodity produced,
we have equilibrium at a certain price which is
implicitly agreed apon, and there is no change in
inventory. The supply and demand equations
can be graphed on the same set of axes, and the
equilibrium point is where they intersect. We
will show price on the vertical axis and quantity
on the horizontal axis, but for the demand curve
x represents xp and for the supply curve x
represents xc.
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EXAMPLE 1.23
x items sold per day when x 1000 are sold,
the price is demand p 10 when x 1700 are
sold, the price is demand p 8 Therefore the
slope of the (straight line) demand is
And the demand equation is
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EXAMPLE 1.24
x billions of pounds sold demand p
55.9867 - 0.2882 x dol/cwt supply p
0.0865 x dol/cwt Price equilibrium occurs when
demand p supply p or demand p -
supply p 0 55.9867 - 0.2882 x 0.0865
x (.2882 0.0865) x 55.9687
collecting like terms x 55.9687 / .3747
149.37 billion pounds So the equilibrium price
is S(x) 0.0865 (149.37) 12.92 dollars
per cwt
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DEMAND-SUPPLY DIFFERENCE
To Calulate the break-even quantity using EXEL's
Goal Seek, we must first compute the formula for
the difference between the demand price and the
supply price. demand p - supply p (55.9867
- 0.2882 x) - 0.0865 x 55.9867 -
(0.2882 0.0865) x 55.9867 - 0.3747 x
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LOOK FOR Goal Seek

• OPEN EXCEL
• Enter x, P(x), and the formula for P(x)
• Choose Tools gt Goal Seek
• If Goal Seek is on the menu, skip the next two
  slides
• Otherwise install Goal Seek this way
• Choose Tools gt Add-Ins
• Check Solver Add-In
• Click on OK

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USE Goal Seek
Piascik, page 20

• Enter the labels x, demandsupply and the
• Enter the formula for demand p supply p
• Choose Tools gt Goal Seek
• Set Cell B2
• To value 0
• By changing cell A2
• Choose OK
• Read break-point quantity 149.42

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Straight Line DEPRECIATION 1.25
initial value 100k dollars at t
0 useful life 10 years salvage value
5k dollars at t 10 Straight Line
EQUATION V m t b
V 100k -9.5k t 0 V 100k -
9.5k t thousand dollars per year
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Graphing Straight-Line Depreciation
V
100
m -9.5 thousand dollars per year
5
t
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