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Chapter 8: Competitive Firms and Markets (4) (Perfect Competition (A…
Chapter 8: Competitive Firms and Markets (4)
Perfect Competition
A market is
competitive
if each firm in the market is a
price taker
Price taker
: a firm that cannot significantly affect market prices for its inputs and outputs
Price taker firm has demand curve that is horizontal at market price
Conditions for price taking behaviour (market with all these conditions is a
perfectly competitive market
)
Firm sell
identical products
Buyers and seller have
full information
Large number of buyers and sellers
Negligible transaction costs
Firms
freely enter and exit
the market
Many markets are reasonably close to competitive
Residual demand curve
Residual demand
: Piece of pie leftover (one firm) after all other firms have sold their products. Market demand that is not met by other sellers at any given price.
Residual demand
Dr(p) = D(p) - So(p)
Dr(p) = residual demand
D(p) = demand of all firms
So(p) = supply of other firms in markets
Residual demand elasticity
Market elasticity of demand
𝜺 = (dD/D) / (dp/p)
𝜺 = dD/dp p/d
𝜺 = market elasticity of demand
(dD/D) = change in demand
(dp/p) = change in price
Residual elasticity for one firm
𝜺i = n𝜺 - (n-1)𝛈o
𝜺i = elasticity of demand facing firm i
n = number of firms
𝜺 = elasticity of market demand
𝛈o = elasticity of supply of other firms
High elasticity means
Firm can sell as much as it wants at market price (no need to offer much lower price)
Firm can hardly sell anything if it raises price above market price
All firms, for reasons above, sell at market price
Single firm: p and q
Market: P and Q
Profit Maximization
Profit maximization determines market price
Economic profit
π = R - C
π = profit
R = revenue
C = costs
Economic profit
includes both explicit and implicit costs
A firm's profit function
π(q) = R(q) - C(q)
C(q) is cheapest way to produce output q (includes cost minimization)
To maximize profits, firms must decide:
Output decision
: If produce, at what level of output q*?
dπ/dq = 0 (marginal profit)
Shutdown decision
: More profitable to produce q* or shutdown?
Short run
: shutdown if R < VC
Long run
: shutdown if R < C
Output rules
Firm sets output where marginal profit is zero
dπ/dq = 0
dπ/dq = marginal profit
dπ/dq = dR/dq - dC/dq = MR - MC
Firm sets output where marginal revenue equals marginal cost
MR = MC
p = MR = MC = demand curve
MR = dR/dq = marginal revenue
MC = dC/dq = marginal cost
R = pq, so dR/dq = p, hence p = MR
Firm sets output where profit is maximized
dπ/dq = 0
Shutdown rules
Firm will shutdown if it can reduce its loss by doing so.
In short run, fixed cost not avoidable.
Shutdown if losses > fixed cost.
R < VC
In long run, shutdown if losses < total cost.
R < C
In both short run and long run, firm will shut down if its revenue is less than its avoidable cost
π = R - C. If R < C, then π < 0. Shutdown.
Competition in the Short Run
Short run profit maximization
Short run shutdown decision
Shutdown if
p < AVC
p < AVC where AVC = VC/q
p < VC/q
pq < VC where R = pq
R < VC
Note: p < min(AVC) means same thing equation is linear, because p = MR = MC, and MC crosses at minimum of AVC
Short run output decision
Because it faces a horizontal demand curve, a competitive firm can sell as many units of output as it wants in the market place.
Profit maximizing firm chooses output such that
dπ/dq = 0
MR = MC or p = MC
Since MR = dR/dq = d(pq)/dq = p
Short run supply curve
Short run firm supply curve
Competitive firms' short run supply curve is MC curve above AVC curve
If factor prices increase, supply curve will shift up and left
Short run market supply curve
Identical firms
S = ns or Q = nq
S = market supply
n = maximum number of firms (fixed)
s = supply of an individual firm
The more identical firms produce at a given price, the flatter and more elastic the market supply curve
Firms that differ
Not all firms produce at every price (less firms, less elastic)
Low cost firms supply goods at lower prices. As price rises, higher cost firms start supplying
Short run competitive equilibrium
To find p and Q at short run competitive equilibrium (for linear MC and AVC):
Set
MR = MC
or
p = MC
Set q = 0 in p = MC(q) to get minimum price p (y-intercept)
Qs = nq(p)
Qd = market demand
Qs = market supply
n = number of firms in market
q = firm quantity supplied (based on price)
In equilibrium,
Qd = Qs
Set Qd(p) = Qs(p) to find p, sub p in Qd or Qs to find Q
Elasticities
Market elasticity of demand
𝜺 = (dQd/Qd) / (dp/p)
Market elasticity of suppy
𝛈 = (dQs/Qs) / (dp/p)
Residual demand elasticity for firm
𝜺i = n𝜺 - (n-1)𝛈
Competition in the Long Run
Long run profit maximization
Long run shutdown decision
Shutdown if
π < 0
π < 0 where π = R - C
If π >= 0, can keep running in both short run and long run
Shutdown if
R < C
pq < C where R =pq
p < AC where AC = C/q
Note: p < min(AC) means same thing, because p = MR = MC, and MC crosses at minimum of AC
Long run output decision
Points
Firms choose to maximize profit, same as in short run
All fixed costs avoidable in long run
Costs generally lower in long run (due to flexibility to choose capital stock)
Because it faces a horizontal demand curve, a competitive firm can sell as many units of output as it wants in the market place.
Profit maximizing firm chooses output such that
dπ/dq = 0
MR = MC or p = MC
Since MR = dR/dq = d(pq)/dq = p
Long run supply curve
Long run market supply curve
Competitive market supply curve is horizontal sum of supply curves of individual firms in short run and long run,
but in long run, firms can enter and leave the market
Firms enter markets if they can make long run profits (π >= 0), and exit market to avoid long run losses (π < 0)
Identical firms
Long run market supply curve is flat. It is at the minimum of the long run average cost of identical firms
To determine number of firms in the market in the long run:
Find
AC = C/q
Find q where minimum of average cost
dAC/dq = 0
Sub q back into AC to find p
Qs = Qd
Sub q and p to find n
nq = Qd(p)
Firms that differ
Low cost firms supply goods at lower prices. As price rises, higher cost firms start supplying.
Long run supply curve for firms that differ look like a staircase
When input prices vary with output
Market supply curves slope up/down if input prices non-constant
Markets in which factor prices rise/fall when output increases, long run supply curve slopes even with identical costs and free entry and exit
Increasing cost market
: input prices rise with output, upward slope of supply
Constant cost market
: input prices remain constant as output increases, flat supply curve
Decreasing cost market
: input prices decrease with output, downward slope of supply
Long run firm supply curve
Firm's long run supply curve is the portion of the MC curve above the long run AV minimum
May look very different from short run curve, because firm can choose capital allocation in long run
Long run market equilibrium
Long run competitive equilibrium may be above or below short run competitive equilibrium. They will both be on the same demand curve, just based on where the long and short run supply curves intersect it.
Intersection of long run market supply curve and demand curve determines long run competitive equilibrium