Copyright © Cengage Learning. All rights reserved.

1STRAIGHT LINES

AND LINEAR FUNCTIONS

Warm Up: p. 45 Self-Check Exercises #1

Copyright © Cengage Learning. All rights reserved.

1.4 Intersection of Straight Lines

3

Market Equilibrium

4

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 quantityproduced is equal to the quantity demanded.

5

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.

6

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

7

Market Equilibrium

The point (x0, p0) lies on the supply curve and therefore satisfies the supply equation. At the same time, it also lieson the demand curve and therefore satisfies the demandequation.

Thus, to find the point (x0, p0), and hence the equilibrium quantity and price, we solve the demand and supplyequations simultaneously for x and p.

For meaningful solutions, x and p must both be positive.

8

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 thequantity demanded in units of a thousand.

9

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 = 0for x and p.

10

Applied Example 6 – Solution

Let us use the method of substitution to solve it. As thename 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

cont’d

11

Applied Example 6 – Solution

Next, we substitute this value of p into the second equation, obtaining

52x + 50x – 300 + 45 = 0

102x – 255 = 0

cont’d

12

Applied Example 6 – Solution

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) andthe equilibrium price is $5.83 per thermometer.

cont’d

13

Practice

p. 45 Self-Check Exercises #2c