The demand equation for a certain brand of GPS Navigator is x + 3p - 565 = 0, where x is the quantity demanded per week and p is the wholesale unit price in dollars.
The supply equation is x - 16p + 480 = 0, where x is the quantity the supplier will make available in the market when the wholesale price is p dollars each. Find the equilibrium quantity and the equilibrium price for the GPS Navigators.
a. equilibrium quantity 2,000 units; equilibrium price $55
b. equilibrium quantity 2,000 units; equilibrium price $40
c. equilibrium quantity 400 units; equilibrium price $55
d. equilibrium quantity 400 units; equilibrium price $40
Please help. Thank you
this is just about like the one you posted yesterday. How far do you get?
To find the equilibrium quantity and price for the GPS Navigators, we need to find the values of x and p that satisfy both the demand and supply equations simultaneously.
Given:
Demand equation: x + 3p - 565 = 0
Supply equation: x - 16p + 480 = 0
To find the equilibrium quantity, we need to solve for x, and to find the equilibrium price, we need to solve for p.
Let's start with solving for x.
From the supply equation: x - 16p + 480 = 0
Rearrange the equation to solve for x: x = 16p - 480
Now, substitute this value of x in the demand equation:
16p - 480 + 3p - 565 = 0
Combine like terms: 19p - 1045 = 0
Add 1045 to both sides: 19p = 1045
Divide both sides by 19: p = 55
Now that we have the equilibrium price (p = 55), we can substitute it back into the demand or supply equation to find the equilibrium quantity:
x = 16p - 480
x = 16(55) - 480
x = 880 - 480
x = 400
Hence, the equilibrium quantity is 400 units and the equilibrium price is $55.
Therefore, the correct option is c. equilibrium quantity 400 units; equilibrium price $55.