Lecture 16 Profit Maximization
under perfect competition
1. Market structure
2. Profit maximization under perfect competition
3. Supply and competitive equilibrium in the short run
Market structures
• Perfect competition: many buyers and sellers,
undifferentiated product, no barriers to entry or exit,
perfect information
– Monopolistic competition – similar to perfect competition
but with differentiated products (examples: clothes,
computers, processed foods)
• Monopoly: Single seller, many buyers, barriers to entry
likely (e.g., limited access to inputs, government
approval)
– Oligopoly – Similar to monopoly but with a small number
of firms. May compete (network television stations, mobile
phone companies) or may collude (OPEC)
Conditions for perfect competition
1.
Firms sell a standardized product
2.
Free entry and exit in long run
3.
Firms and consumers have perfect information
4.
Firms are price takers
5.
Large number of buyers and sellers
Almost never perfectly satisfied but often close enough
Product homogeneity
• The product sold by one firm is assumed to be a
perfect substitute for the product sold by any
other
• Classic examples of homogenous products:
agricultural products (corn, wheat, milk, oranges,
beef, sugar), gasoline, steel
– Often called commodities
• Buyers are indifferent among products from
different sellers.
• One price in the market.
Free entry and exit
• No significant cost that makes it difficult for new firms to
enter the industry or existing firms to leave
– Factors of production are mobile in the long run (no entry or
exit in short run by definition)
• Common examples of barriers to entry:
– Licensing requirements—bars, taxis, professions (lawyers,
doctors, veterinarians), pro sports teams
– Access to inputs or use of technology (limited supply, patent;
cost)
• Examples of barriers to exit:
– Labor contracts –can’t afford to close because costs of paying
off contracts are too high
– In some countries, agricultural land that is unused is subject to
expropriation
Perfect information
• Firms know all the possible profit
opportunities in the industry and elsewhere.
• Consumers know all the prices charged by
firms and the product information
Firms are price takers
• The firm has no control over the price of the
products they sell. They sell at the price
determined in the market.
– Most important condition
– Follows from homogeneity and free entry and
exit, no firm could sell at a price other than the
market price and stay in business.
Large number of buyers and sellers
• Follows from others but is well-known and is
easy to verify empirically (though there is no
definition of “large”)
• The number of buyers and sellers is large in
the sense that no individual firm can
significantly affect the price of the product by
changing the quantity it buys or sells.
Definition of profit (π)
• Profit = Economic profit = total revenue minus
total costs, where total cost includes implicit
and explicit costs
– π =TR (Q) – TC (Q)
• Accounting profits = TR - explicit costs
• Accounting profit > Economic profit
– Difference between economic profit and
accounting profit is often called “normal profit”
which is the opportunity cost of owner’s resources
Profit in short and long run under
perfect competition
• π = TR(Q) – TC (Q)
• π = PQ – TC (Q) = PQ – (TC/Q)Q
– TR = PQ because firm is a price taker
– In short run: π = Q (P - ATC)
– In long run, π = Q(P - LAC)
Example: Calculating total revenue, cost and profit
The following table contains firm output and cost data.
(Is this short or long run?)
Q
TC
AVC
ATC
MC
0
30
--
--
--
1
55
2
62
3
70
4
80
5
91
6
105
7
125
8
147
9
170
10
200
TR
Profit
In Class 1- Calculate Marginal Cost
Q
TC
AVC
ATC
MC
0
30
--
--
--
1
55
25.0
55.0
2
62
16.0
31.0
3
70
13.3
23.3
4
80
12.5
20.0
5
91
12.2
18.2
6
105
12.5
17.5
7
125
13.6
17.9
8
147
14.6
18.4
9
170
15.6
18.9
10
200
17.0
20.0
TR
Profit
MC, ATC and AVC
$
60.0
50.0
40.0
MC
30.0
ATC
20.0
AVC
10.0
0.0
1
2
3
4
5
6
7
8
9
10
Q
Graph of profit as a function of Q
$
20
10
0
1
2
3
4
5
6
7
8
9
10
11
-10
-20
-30
-40
Q
Total revenue, total cost and profit for a typical firm
Marginal revenue, marginal cost and profit
• π = TR(Q) – TC (Q)
• A condition for π maximization is ∂π/∂Q = 0
• ∂π/∂Q = ∂TR/∂Q - ∂TC/∂Q
– Marginal revenue (MR) is the change in revenue from
the sale of an additional unit of Q
• ∂TR/∂Q
• When firm is a price taker, MR=P since ∂TR/∂Q =∂PQ/∂Q=P
– Marginal cost (MC) is the change in total cost from an
additional unit of Q
• ∂TC/∂Q
Marginal revenue, marginal cost and profit
• Under perfect competition, maximum profit
occurs when MR=MC => P=MC
– ∂π/∂Q = MR - MC = 0 => MR=MC
– This is equivalent to marginal benefit = marginal
cost
Profit-Maximizing Output Level in the
Short-Run
Profit maximization under perfect
competition
• Output rule in the Short‐run: If a firm is
producing any output, Q should be set at the
level where MC (Q) = P on the rising portion of
the MC curve.
• Output rule in the Long‐run: If a firm is
producing any output, Q should be set at the
level where LMC(Q) = P on the rising portion
of the LMC curve.
The output rule of profit maximization
• If the firm is producing any output (Q), to maximize profits the
firm should produce a level of output for which marginal
revenue is equal to marginal cost on the rising portion of the
MC curve (see thick line in graph)
• Output rule applies in the short and long run.
Shut-down rules under perfect
competition
• Shut‐down Rule in the Short‐run: The firm
should shut down (produce nothing) if P <
minimum average variable cost (min AVC).
• Shut‐down Rule in the Long‐run: The firm
should shut down (produce nothing) if P<
minimum average total cost (min LAC).
Shut-down Rule in the short run: The firm
should shut down (produce nothing) if P <
minimum average variable cost (min AVC).
P
Problem here is that firm is not covering variable costs
The “shut down” rule
• At any level of Q, if P < AVC, π < − FC
• π = PQ − TC = PQ − VC − FC which can be rewritten as Q(P-AVC) − FC
• If P < AVC, then Q(P-AVC) <0 and π < -FC
• If Q=O, then π = − FC so firm will maximize
profit by producing nothing.
In class 2 – How much would the firm produce
when P = 30? when P = 20? and when P = 10?
$
60.0
50.0
40.0
MC
30.0
ATC
20.0
AVC
10.0
0.0
1
2
3
4
5
6
7
8
9
10
Q
Finding Q* to maximize profit using
cost function
• A firm’s cost function (TC) = Q2- 4Q+10 and
price is 20. If firm is maximizing profit,
– What will its output (Q) be?
– What will its profit be?
Find Q* to maximize profit
•
•
•
•
TC = Q2-4Q+10 and P = 20
Profit is maximized when MR=MC or P=MC
MC= ∂TC/∂Q = 2Q-4
Set MC equal to 20 and solve for Q.
– 2Q-4 = 20 => Q=12
If Q*=12, what is profit?
•
•
•
•
•
TC = Q2-4Q+10 and price = 20.
Profit = TR-TC
TR = PQ= 20*12 = 240
TC= 122-4(12)+10 = 144-48+10 = 106
Profit = TR-TC = 240-106 = 134
In class 3
• A firm’s cost function is TC = Q2-4Q+10 and
price is 6. If firm is maximizing profit,
– What will its output (Q) be?
– What will its profit be?
In the short run, the individual firm will maximize
profit by producing Q where MR=MC when
P is > AVC and Q=0 when P ≤ AVC
In the long run, the individual firm will maximize
profit by producing Q where MR=LMC when
P is ≥ LAC and Q=0 when P< LAC
Key differences between short and
long run
• In the short run, a firm might still produce Q>0 even
though profits are negative as long as π > -FC.
• If -FC> π then firm should shut down (produce Q=0).
– It would still have to pay fixed costs but is better off
producing nothing and waiting to see if P increases
• A farmer can leave crops in the field if expected profit is less than
fixed costs
• Firms can stop production and lay off wage laborers but still pay
salaries
• In the long run, there are no fixed costs so if π <0, firm
should shut down permanently.
Firm supply curve in the short run (SR)
•
•
Supply curve
records results of
firm’s profit
maximization
decisions
In a perfectly
competitive
market, firm SR
supply curve is the
portion of the MC
curve that is above
AVC and the
portion of Y axis
(Q=0) that is
below the
minimum AVC.
Industry and market supply functions
• Firm Supply (Curve/Function): the
relationship between the price of a product
and the quantity of the product supplied by
one individual firm.
• Market / Industry Supply (Curve/Function):
the relationship between the price of a
product and the total quantity of the product
supplied by all firms in the market.
Market supply function is the horizontal sum of
the individual firm supply functions
In class 4
• In the peanut butter industry, there are 100
identical firms and each has a supply function
P=4+Qi. What is the industry supply function?
Competitive equilibrium (market equilibrium in
a perfectly competitive market)