Supply and Demand of Wireless External Hard Drives

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Lesson Parent: 
Supply and Demand Functions
Problem: 

Determine the equilibrium price and quantity of wireless external hard drives if their demand function is $p_d(n)=112-1.29\times 10^{-4}n$ and their supply function is $p_s(n)=2\times 10^{-10}n^2+23$.

Answer: 

SAMPLE SOLUTION

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Solution: 

The equilibrium quantity $n'$ is found by setting <Sign in to see all the formulas>. First, let's do the algebra to find $n'$.

<Sign in to see all the formulas>

This is a Quadratic Equation whose solution can be found with our Quadratic Equation Solver:



<Sign in to see the interactive form>

We find that the solutions are <Sign in to see all the formulas> and <Sign in to see all the formulas>.

We will reject the solution <Sign in to see all the formulas>. This is because selling a negative number of drives does not make sense. This would mean we are buying the hard drives. The solution <Sign in to see all the formulas> makes sense graphically. See the graph below where the supply and demand curves cross at <Sign in to see all the formulas> drives.

Now with <Sign in to see all the formulas> (note that we have rounded because you can't buy or sell part of a hard drive) we can put it into either <Sign in to see all the formulas> or <Sign in to see all the formulas> to determine the equilibrium price. Let's put it into both to demonstrate that the price comes out the same. First for <Sign in to see all the formulas>:

<Sign in to see all the formulas>


Now for <Sign in to see all the formulas>:

<Sign in to see all the formulas>

Therefore, both consumers and producers will agree to buy and sell <Sign in to see all the formulas> wireless external hard drives at a price of $\$$58.02.