Question

The demand equation for the Drake GPS Navigator is x + 4p − 848 = 0, where x is the quantity demanded per week and p is the wholesale unit price in dollars. The supply equation x − 20p + 1000 = 0, where x is the quantity the supplier will make available in the market each week when the wholesale price is p dollars each. Find the equilibrium quantity and the equilibrium price for the GPS Navigators.

Answer 1

Given:

Demand equation :
`x+4p-848=0`.

Supply equation :
`x-20p+1000=0`

To find:

The equilibrium quantity and the equilibrium price for the GPS Navigators.

Solution:

Demand equation is

`x+4p-848=0`

where x is the quantity demanded per week and p is the wholesale unit price in dollars.

Quantity demanded
`=x=848-4p` ...(i)

Supply equation is

`x-20p+1000=0`

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
`=x=-1000+20p` ...(ii)

For equilibrium, Quantity demanded = Quantity supplied.

`848-4p=-1000+20p`

`848+1000=4p+20p`

`1848=24p`

Divide both sides by p.

`(1848)/(24)=p`

`77=p`

Substitute p=77 in (i), to find the equilibrium quantity.

`x=848-4(77)`

`x=848-308`

`x=540`

Therefore, the equilibrium quantity is 540 units per week and the equilibrium price is $77 for the GPS Navigators.