Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p = pN - 0.1Q, where p is the price per pair of replacement tips, pN is the price of a new pair of headphones, and Q is the number of tips per week. Suppose that the inverse supply function of the replacement tips is p = 2 + 0.012 Q. a. The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips ( dp/dpN) at the equilibrium is given by nothing (Round your answer to three places.)

Complete Question

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a

   The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips ( dp/dpN) is

b

 The value of Q and p at equilibruim is

             and     5

The consumer surplus is  

The producer surplus  is  

Explanation:

      From the question we are told that

           The inverse market demand is  

                The inverse supply function is    

a

The effect of change in the price  is mathematically given as

Now differntiating the inverse market demand function with respect to

We get that  

b

   We are told that $30

        Therefore the inverse market demand becomes

At  equilibrium

So we have

Where is the quantity at equilibrium

Substituting the value of  Q into the equation for the inverse market demand function

                    5

Looking at the equation for we see that

     For  Q =  0

 And  for Q =  250

Hence the consumer surplus is mathematically evaluated as

Substituting value

And

  The  producer surplus is mathematically evaluated as

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