Supply and Demand of Wireless External Hard Drives
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Determine the equilibrium price and quantity of wireless external hard drives if their demand function is pd(n)=112−1.29×10−4n and their supply function is ps(n)=2×10−10n2+23.
SAMPLE SOLUTION
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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>:
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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.
