2. Worldwide annual sales of all cell phones is approximately -10p + 1600 million phones when the wholesale price is $p.
a) If manufacturers are prepared to supply q = 14p – 800 million phones per year at a wholesale price $p, what would be the equilibrium price?
-10p +1600 = 14p -800
+10p +10p
1600 = 24p -800
+800 +800
2400 = 24p
/24 /24
$100 = p
b) The actual wholesale price was projected to be $80 in the fourth quarter of 2011. Estimate the projected shortage or surplus.
-10p +1600 = X
-10(80) +1600 = X
-800 +1600 = X
800 = X
The projected surplus is 800 million phones.
b) The projected shortage or surplus would be 800 million phones.
a) To find the equilibrium price, we need to set the supply equal to the demand and solve for p.
Demand: Worldwide annual sales of all cell phones is given by -10p + 1600 million phones.
Supply: Manufacturers are prepared to supply q = 14p - 800 million phones per year.
Setting the demand equal to the supply:
-10p + 1600 = 14p - 800
Adding 10p to both sides:
1600 = 24p - 800
Adding 800 to both sides:
2400 = 24p
Dividing both sides by 24:
p = $100
Therefore, the equilibrium price is $100.
b) To estimate the projected shortage or surplus, we can substitute the wholesale price into the demand equation.
Demand: -10p + 1600 million phones
Substituting p = $80:
-10(80) + 1600 = X
-800 + 1600 = X
800 = X
Therefore, the projected shortage or surplus would be 800 million phones.
To find the equilibrium price in part a), we are given the equation -10p + 1600 = 14p - 800. We want to solve for p, so we can start by adding 10p to both sides of the equation to eliminate the -10p term:
-10p + 1600 + 10p = 14p -800 + 10p
This simplifies to:
1600 = 24p - 800
Next, add 800 to both sides of the equation to eliminate the -800 term:
1600 + 800 = 24p - 800 + 800
This simplifies to:
2400 = 24p
To solve for p, divide both sides of the equation by 24:
2400/24 = 24p/24
This simplifies to:
100 = p
Therefore, the equilibrium price is $100.
In part b), we are given that the projected wholesale price is $80. To find the projected shortage or surplus, we substitute the value of p into the equation -10p + 1600 = X:
-10(80) + 1600 = X
This simplifies to:
-800 + 1600 = X
800 = X
Therefore, the projected shortage or surplus is 800 million phones.