Topic 7. Perfectly Competitive Markets

 

Perfect Competition

      The behavior of firms and the determination of price and output depend on the market structures.  We now consider a market structure called perfect competition.  A market is in perfect competition if it satisfies the following conditions:

(1) Firms in the market all produce the same product.

(2) Each market participant is small enough so that the market price will not be affected by his or her actions.

(3) Perfect information.

(4) Free entry and exit.

      Although perhaps no market will completely satisfy these conditions, perfect competition serves as a useful benchmark in economic analysis.

 

Price Determination in the Short-run           

      First,  we need to know how an individual firm determines its output.   The firm's profit is

Π(x) = TR(X) - TC(X) 

 Since the firm takes market price as given, its marginal revenue is equal to p.  The profit-maximizing output is the one at which marginal cost is equal to marginal revenue, which is in turn equal to p.

      What happens if at the profit-maximizing output, the firm is actually having a loss?  Should the firm stop production?  The answer is that it depends on whether the price is higher than the average variable cost.  If price is higher than average variable cost, the firm should produce the output at which marginal cost equals price, and if price is lower than the average variable cost, the firm should shut down.  Note that the marginal cost curve passes through the minimum point of the average variable cost curve.

      This allows us to derive the output supplied by a firm in a market with perfect competition as a function of the market price, that is, the short-run supply function (curve) of an individual firm.  When price is lower than the average variable cost, the firm produces zero output.  When price is higher than the average variable cost, the firm's supply curve coincides with its marginal cost curve.

 Example.  If a firm has VC = x2   and MC = 2x, what will be the function of its supply curve?

         

Next, we can derive the short-run supply curve of an industry.  It is the horizontal summation of all firms' supply curves in the industry.

Example.  If each firm's supply function is q = p/2, and there are 100 identical firms in the industry, what will the industry supply curve?

      Finally, we can determine the shore-run equilibrium price and quantity in the market.  This occurs when quantity demanded is equal to the quantity supplied.

Example. Suppose market demand is Q = 600 - 10p, and market supply is Q = 50p.  What will be equilibrium price and output on the market?  If each firm VC = x2, what will be the output of each firm?  What will be the profit of each firm if FC = 20? 

Example.  Suppose the government decides to charge or to increase license fees for restaurants (or the local government imposes a property tax on restaurants).  A restaurant previously making money may now lose money, but it might continue to operate in the short-run. 

 

Price Determination in the Long-run

      In the long-run, firms will still produce the output at which long-run marginal cost equates price.  However, now if price is higher than average cost, so that an incumbent firm makes positive profit, more firms will enter the industry.  As more firms enter, the industry supply curve will shift to the right, which will lower the market price.

      Therefore, in the long-run, firms in a perfectly competitive market earn zero economic profit.  It follows that all firms must produce at the point where average cost is minimized, and price is equal to the average cost.

Example.  In a competitive industry, suppose each firm has identical cost functions as follows:

          LTC(q) = 200 + 10X + 2X2     and

          MC(q) = 10 + 4X

The industry demand is:         Q = 800 - 8p

Suppose the industry is in long-run competitive equilibrium:

(a) Find the level of output produced by each firm.

(b) Find the industry price.

(c) Find industry output.

(d) Determine the number of single-plant firms in the industry.

The shape of the long-run industry supply curve depends on how the entry of new firms will affect the cost function of a typical firm in the industry. 

      If the cost function of a typical firm of the industry will not be affected by the entry of new firms, then the industry is called a constant-cost industry.  For a constant-cost industry, its long-run industry supply curve is horizontal.

      If the cost of a typical firm of the industry increases as more firms enter the industry, as a result of, say, higher input prices as more inputs are used by the industry, then the industry is called an increasing-cost industry.  For such an industry, its long-run supply curve is up-ward sloping.

      If the cost of a typical firm of  the industry decreases as more firms enter the industry, the industry is called a decreasing-cost industry.  External economies is the reason for the existence of decreasing-cost industries.  For a decreasing-cost industry, its long-run supply curve is downward slopping.

      To measure how quantity supplied will respond to price changes, we often use price elasticity of supply, which is defined as the percentage change in quantity supplied that is caused by one percent change in price.  Of course, the short-run price elasticity of supply is lower than the long-run price elasticity of supply.

 

Example: Perfectly inelastic supply curve and perfectly elastic supply curve

 

Example.  Suppose that the price elasticity of demand for beef is 0.9, and the price elasticity of supply for beef is 1.5 in the long-run in the U.S..  Further assume that the industry is currently in long-run equilibrium.  Now suppose as a result of trade negotiation, some foreign countries are lowering their trade barriers and begin to import more beef from the U.S.  Consequently, the domestic price for beef is increased by 1% in the long-run.  What would be the percentage changes of beef quantities supplied and demanded in the U.S.? 

 

Producer Surplus

Producer surplus is the difference between the revenue a firm receives at certain output level and the payment that is required for the firm to be willing to supply this output. It is the area between the supply curve and the market price.

 

PS = TR – TVC – nonsunk FC

 

In the short run, PS = economic profit + sunk fixed cost

In the long run: PS = economic profit

 

Efficiency of a perfectly competitive Market:

 

Applications:

 

--Impact of an excise tax

 

--Production subsidies

 

--Price ceiling (maximum price regulation)

 

--Price floors (minimum price regulation)

 

--Import tariffs and quotas