Perfect Competition, Linear Equilibrium

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Equation / Last modified by KurtHeckman on 2017/08/23 12:33
`Qd = `
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AustinS.Perfect Competition, Linear Equilibrium
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Perfect competition is a term used to describe markets that are perfectly competitive.  In markets that are perfectly competitive, all firms are price takers and the total long-run equilibrium economic profit is equal to zero.


Five Characteristics of a Perfectly Competitive Market

  1. All firms produce and sell identical products.
  2. There are many buyers and sellers in the market.
  3. Market participants have perfect information about price and products
  4. Transaction costs are zero or negligible.
  5. Firms are able to easily enter and exit the market.

Supply and Demand Curves

In perfectly competitive industries a market's supply and demand functions can generally be represented linearly by the following equations,

      Market Demand:   Qd(p)  = A – Bp

      Market Supply:     Qs(p)  = C + Dp

the functions above show the relationship between the price of a good and the quantity demanded by consumers and the quantity supplied by producers.  

The application and analysis of a market's supply and demand curves reveal many important attributes of the market. In solving the system of equations composed of the market supply and demand curves, the market equilibrium price and quantity can be found: p* and Q*

Supply and Demand EQ.png

Inputs

Suppose that the perfectly competitive market for a particular good can be represented by the general linear supply and demand functions in the following notation in which everything is in terms of quantity,

                Qs  = C + Dp and Qd  = A – Bp

For example if the market for bluetooth speakers is represented by the supply and demand functions,

                Qs = 30000 + 100p and Qd = 370000 - 875p

then the following would be inputted into the above calculator

A370000
B875
C30000
D100

Explanation

In entering the above supply and demand curves into the calculator above, we get the following equilibrium for the bluetooth speaker market,

        Equilibrium Price (p*):          $348.72

        Equilibrium Quantity (Q*):    64871.79

At a price of $348.72 the bluetooth speaker market is perfectly efficient and social welfare is maximized.


References

Perloff, Jeffrey. Microeconomics. Boston, MA: Pearson Education, 2011. Print.