Modeling Firms

1
Modeling Firms Behavior

• Most economists treat the firm as a single
  decision-making unit
• the decisions are made by a single dictatorial
  manager who rationally pursues some goal
• profit-maximization

2
Profit Maximization

• A profit-maximizing firm chooses both its inputs
  and its outputs with the sole goal of achieving
  maximum economic profits
• seeks to maximize the difference between total
  revenue and total economic costs

3
Output Choice

• Total revenue for a firm is given by
• TR(q) P(q)?q
• In the production of q, certain economic costs
  are incurred TC(q)
• Economic profits (?) are the difference between
  total revenue and total costs
• ? TR(q) TC(q) P(q)?q TC(q)

4
Output Choice

• The necessary condition for choosing the level of
  q that maximizes profits can be found by setting
  the derivative of the ? function with respect to
  q equal to zero

5
Output Choice

• To maximize economic profits, the firm should
  choose the output for which marginal revenue is
  equal to marginal cost

6
Profit Maximization
revenues costs
TC
TR
output
7
Marginal Revenue

• If a firm can sell all it wishes without having
  any effect on market price, marginal revenue will
  be equal to price
• If a firm faces a downward-sloping demand curve,
  more output can only be sold if the firm reduces
  the goods price

8
Marginal Revenue

• If a firm faces a downward-sloping demand curve,
  marginal revenue will be a function of output
• If price falls as a firm increases output,
  marginal revenue will be less than price

9
Marginal Revenue

• Suppose that the demand curve for a sub sandwich
  is
• q 100 10P
• Solving for price, we get
• P -q/10 10
• This means that total revenue is
• TR Pq -q2/10 10q
• Marginal revenue will be given by
• MR dTR/dq -q/5 10

10
Profit Maximization

• To determine the profit-maximizing output, we
  must know the firms costs
• If subs can be produced at a constant average and
  marginal cost of 4, then
• MR MC
• -q/5 10 4
• q 30

11
Average Revenue Curve

• If we assume that the firm must sell all its
  output at one price, we can think of the demand
  curve facing the firm as its average revenue
  curve
• shows the revenue per unit yielded by alternative
  output choices

12
Marginal Revenue Curve

• The marginal revenue curve shows the extra
  revenue provided by the last unit sold
• In the case of a downward-sloping demand curve,
  the marginal revenue curve will lie below the
  demand curve

13
Marginal Revenue Curve
As output increases from 0 to q1, total revenue
increases so MR gt 0
price
As output increases beyond q1, total revenue
decreases so MR lt 0
P1
D (average revenue)
output
q1
MR
14
Marginal Revenue Curve

• When the demand curve shifts, its associated
  marginal revenue curve shifts as well
• a marginal revenue curve cannot be calculated
  without referring to a specific demand curve

15
Short-Run Supply by a Price-Taking Firm
price
SMC
SATC
SAVC
output
16
Short-Run Supply by a Price-Taking Firm
price
SMC
SATC
P MR
SAVC
output
q
17
Short-Run Supply by a Price-Taking Firm
price
SMC
SATC
P MR
SAVC
output
q
18
Short-Run Supply by a Price-Taking Firm
price
SMC
SATC
P MR
SAVC
profit maximization requires that P SMC and
that SMC is upward-sloping
output
q
? lt 0
19
Short-Run Supply by a Price-Taking Firm

• The positively-sloped portion of the short-run
  marginal cost curve is the short-run supply curve
  for a price-taking firm
• it shows how much the firm will produce at every
  possible market price
• firms will only operate in the short run as long
  as total revenue covers variable cost
• the firm will produce no output if P lt SAVC

20
Short-Run Supply by a Price-Taking Firm

• Thus, the price-taking firms short-run supply
  curve is the positively-sloped portion of the
  firms short-run marginal cost curve above the
  point of minimum average variable cost
• for prices below this level, the firms
  profit-maximizing decision is to shut down and
  produce no output

21
Short-Run Supply by a Price-Taking Firm
price
SMC
SATC
SAVC
output
22
Supply Function

• The supply function for a profit-maximizing firm
  that takes both output price (P) and input prices
  (v,w) as fixed is written as
• quantity supplied q(P,r,w)
• this indicates the dependence of output choices
  on these prices

23
Supply Function

• The supply function provides a convenient
  reminder of two key points
• the firms output decision is fundamentally a
  decision about hiring inputs
• changes in input costs will alter the hiring of
  inputs and hence affect output choices as well

24
Producer Surplus in the Short Run

• A profit-maximizing firm that decides to produce
  a positive output in the short run must find that
  decision to be more favorable than a decision to
  produce nothing
• This improvement in welfare is termed (short-run)
  producer surplus
• what the firm gains by being able to participate
  in market transactions

25
Producer Surplus in the Short Run
SMC
price
output
26
Producer Surplus in the Long Run

• By definition, long-run producer surplus is zero
• fixed costs do not exist in the long run
• equilibrium profits under perfect competition
  with free entry are zero