Download 1.4 Intersection of Straight Lines

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STRAIGHT LINES
AND LINEAR
FUNCTIONS
Warm Up: p. 45 Self-Check Exercises
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1.4
Intersection of Straight Lines
Copyright © Cengage Learning. All rights reserved.
Market Equilibrium
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Market Equilibrium
Under pure competition, the price of a commodity
eventually settles at a level dictated by the condition that
the supply of the commodity be equal to the demand for it.
If the price is too high, consumers will be more reluctant to
buy, and if the price is too low, the supplier will be more
reluctant to make the product available in the marketplace.
Market equilibrium is said to prevail when the quantity
produced is equal to the quantity demanded.
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Market Equilibrium
The quantity produced at market equilibrium is called the
equilibrium quantity, and the corresponding price is called
the equilibrium price.
From a geometric point of view, market equilibrium
corresponds to the point at which the demand curve and
the supply curve intersect.
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Market Equilibrium
In Figure 39, x0 represents the equilibrium quantity and
p0 the equilibrium price.
Market equilibrium is represented by the point (x0, p0).
Figure 39
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Market Equilibrium
The point (x0, p0) lies on the supply curve and therefore
satisfies the supply equation. At the same time, it also lies
on the demand curve and therefore satisfies the demand
equation.
Thus, to find the point (x0, p0), and hence the equilibrium
quantity and price, we solve the demand and supply
equations simultaneously for x and p.
For meaningful solutions, x and p must both be positive.
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Applied Example 6 – Market Equilibrium
The management of ThermoMaster, which manufactures
an indoor–outdoor thermometer at its Mexico subsidiary,
has determined that the demand equation for its product is
5x + 3p – 30 = 0
where p is the price of a thermometer in dollars and x is the
quantity demanded in units of a thousand.
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Applied Example 6 – Market Equilibrium
The supply equation for these thermometers is
52x – 30p + 45 = 0
where x (measured in thousands) is the quantity that
ThermoMaster will make available in the market at p dollars
each. Find the equilibrium quantity and price.
Solution:
We need to solve the system of equations
5x + 3p – 30 = 0
52x – 30p + 45 = 0
for x and p.
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Applied Example 6 – Solution
cont’d
Let us use the method of substitution to solve it. As the
name suggests, this method calls for choosing one of the
equations in the system, solving for one variable in terms of
the other, and then substituting the resulting expression
into the other equation. This gives an equation in one
variable that can then be solved in the usual manner.
Let’s solve the first equation for p in terms of x. Thus,
3p = –5x + 30
p = – x + 10
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Applied Example 6 – Solution
cont’d
Next, we substitute this value of p into the second equation,
obtaining
52x + 50x – 300 + 45 = 0
102x – 255 = 0
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Applied Example 6 – Solution
cont’d
The corresponding value of p is found by substituting this
value of x into the equation for p obtained earlier. Thus,
We conclude that the equilibrium quantity is 2500 units
(remember that x is measured in units of a thousand) and
the equilibrium price is $5.83 per thermometer.
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Practice
p. 45 Self-Check Exercises #2c
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