Economics, 3rd Edition

32

− 3p = 20 + 4p

Subtract 20 from both sides and add 3p to both sides to get:

32

− 20 = 4p + 3p

12

= 7p

P = €1.71(

 

rounded to the nearest whole cent

 

)

We can now substitute the equilibrium price into our two equations to find the equilibrium quantity 

rounded to the nearest whole number:

Qd = 32 − 3p

Qd = 32 − 3(1.71)

Qd = 32 − 5.13

Qd = 26.87

Qd = 27

As a check, follow the same process with the supply equation:

Qs = 20 + 4p

Qs = 20 + 4(1.71)

Qs = 20 + 4(1.71)

Qs = 26.84

Qs = 27

Note the figures for Qd and Qs before rounding differ slightly because we had to round the price.

Now look at this example:

P = 3 + 0.25Qs

P = 15 − 0.75Qd

In this case the equations are defined in terms of price but the principle of working out equilibrium is 

the same as we have used above.

First, set the two equations equal to each other:

3

+ 0.25Qs = 15 − 0.75Qd

Then solve for Q by adding 0.75Qd to both sides and then subtract 3 from both sides to get:

0.75Qd + 0.25Qs = 15 − 3

                   Q = 12

Substitute Q

= 12 into one of the equations to find P.

P = 3 + 0.25Qs

P = 3 + 0.25(12)

P = 6

To check, also substitute into the demand equation:

P = 15 − 0.75Qd

P = 15 − 0.75(12)

P = 15 − 9

P = 6

---

CHAPTER 3  THE MARKET FORCES OF SUPPLY AND DEMAND  61

Finding Market Equilibrium – The Elimination Method 

There is another way to find both the quantity 

and the price and that is through adopting the approach of solving simultaneous equations. Simultaneous 

equations require us to find two or more unknowns. In our case the two unknowns are price and quantity.

Look at the following two equations: