Given:
Demand equation : [tex]x+4p-848=0[/tex].
Supply equation : [tex]x-20p+1000=0[/tex]
To find:
The equilibrium quantity and the equilibrium price for the GPS Navigators.
Solution:
Demand equation is
[tex]x+4p-848=0[/tex]
where x is the quantity demanded per week and p is the wholesale unit price in dollars.
Quantity demanded [tex]=x=848-4p[/tex] ...(i)
Supply equation is
[tex]x-20p+1000=0[/tex]
where x is the quantity the supplier will make available in the market each week when the wholesale price is p dollars each.
Quantity supplied [tex]=x=-1000+20p[/tex] ...(ii)
For equilibrium, Quantity demanded = Quantity supplied.
[tex]848-4p=-1000+20p[/tex]
[tex]848+1000=4p+20p[/tex]
[tex]1848=24p[/tex]
Divide both sides by p.
[tex]\dfrac{1848}{24}=p[/tex]
[tex]77=p[/tex]
Substitute p=77 in (i), to find the equilibrium quantity.
[tex]x=848-4(77)[/tex]
[tex]x=848-308[/tex]
[tex]x=540[/tex]
Therefore, the equilibrium quantity is 540 units per week and the equilibrium price is $77 for the GPS Navigators.
