## Example: Equilibrium price

The demand and supply curves in the $q$ market are given by:

$Q_{d} =100 - 2 \cdot p \quad \quad Q_{s} = p - 8$

• How much $q$ good will consumers demand if the price is $p=40$ ? Sol.
$Q_{d}(40)=100-2 \cdot 40 = 20$
They demand 20 units
• And how much will the producers offer? Sol.
$Q_{s}(40)=40- 8 = 32$
They offer 32 units
• What happens in this case in the market? Sol.
Some producers cannot sell everything they want, they cannot find a buyer.
• What if the price was $p=30$? Sol.
Now the amount demanded would be $Q_{d}(30)=100-2\cdot 30=40,$ and the amount offered $Q_{s}(30)= 30-8=22.$ There will not be enough production to supply all the demand.
• Finally, what would happen at $p=36$? Sol.
The demand will be $Q_{d}(36)=100 - 2\cdot 36 = 28,$ and the supply $Q_{s}(36)=36-8 = 28.$ At price 36 the quantity demanded matches the quantity offered. All agents can make their decisions effective.