Transcript OUTPUT AND COSTS - Colorado College

OUTPUT AND COSTS
1. Goals of the Firm
· Profit Maximization
· Sales maximization
· Employment Maximization
2. Constraints facing the firm
· Market Constraints
· Technology Constraints
· Time Constraints
· Short Run
· Long Run
· Fixed Inputs
· Variable Inputs
3. Short run technology constraints and associated concepts
·
·
·
·
Total, Average and Marginal Product
Numerical example
Graphical Exposition
Law of Diminishing Returns
1
Goals of the firm
• Profit Maximization: The firm attempts to
maximize the difference between total
revenue and total cost of production.
• Total Revenue (TR) is the amount earned
from selling the product of the firm. It is
the Dollar value of sales. TR = Price *
Quantity
2
Goals of the firm
• Sales Maximization: The firms’ primary
goal is to maximize the amount of sales.
Profits take a backseat. This may be an
attempt to capture market share through
brand recognition which may be viewed as
a first step towards profit maximization.
Firms may pursue brand recognition for
other reasons such as gaining the
confidence of potential investors.
3
Goals of the firm
• Employment Maximization: The primary
goal of the firm is to maximize the number
of employees. Typically employment
maximization does not go hand in hand with
profit maximization. However, in some
instances pyramid schemes such as Amway
rely on a large number of employees to
compete effectively against firms with
established distribution networks.
4
Constraints facing the firm
·
Market Constraints: They are the price and
quantity constraints that face a firm in the
purchase of inputs (such as land, labor and capital)
and the sale of outputs (the products of the firm).
In other words the firm is bound by market forces
to pay the going wage rate for labor, the going
interest rate for bank loans etc. By the same token
a firm has to price its’ product according to the
market.
5
Constraints facing the firm
• Technological Constraints: Technological
constraints limit how the firm can use inputs
to combine outputs. In other words, it is the
technology that determines how much a
given set of factors of production can
produce.
6
Constraints facing the firm
• For example, a student with access to the
internet and online databases today can
write an excellent term paper in a shorter
amount of time than a student who does not
have access to these resources. Generally
improvements in technology allow the firm
to produce improved products in greater
quantities often in a shorter amount of time
and at lower cost.
7
Constraints facing the firm
• Time Constraints: The amount of time a firm has
to make a decision about inputs (land, labor,
capital etc) or output (amount to be produced) and
the pricing of output. In a challenging business
climate firms often have to make rapid decisions.
It is generally the firms that make good decisions
under pressure or firms that anticipate decisions in
advance that succeed. In economics we divide
time into the short run (SR) and the long run (LR)
8
Constraints facing the firm
•o
Short Run: The short run is a period
of time in which the quantity of at least one
input cannot be changed by the firm. The
firm can change quantities of all other
inputs. For example if a bookstore wanted
to expand into the space next door, it may
take a little time to expand the store.
9
Constraints facing the firm
• Long Run: The long run is a period of time long
enough for the firm to adjust the amounts of all
inputs.
•o
Fixed Inputs: Fixed inputs are those inputs
whose amount cannot be changed by the firm in
the short run. Example: Expanding the book store
to the store next door may not be done in the SR.
•o
Variable Inputs: Variable Inputs are those
inputs whose amount can be easily changed by the
firm in the short run. Example: Hiring new sales
associates to expand the labor force.
10
Total, Average and Marginal
Products
o Total Product: The total product curve shows the
maximum amount of output that can be obtained
from a given amount of the fixed input as the
amount of the variable input is adjusted. For
example the total product curve of a jean factory
would show the maximum amounts of jeans
produced for different amounts of labor and raw
materials given a fixed number of jean machines.
11
Total, Average and Marginal
Products
o Average Product: APL = TP / L The average
product of an input is the total product divided by
the total amount of the variable input used in
production.
•
o Marginal Product: MPL = TP/L The marginal
product of an input is the increase in total output
from an additional unit of the input. For example
the number of jeans produced by one more workhour.
12
Total, Average and Marginal
Products
Labor (L)
Total Product (TP)
Average Product (AP)
Marginal Product (MP)
0
1
2
3
4
5
0
15
34
48
60
62
15/1
34/2
48/3
60/4
62/5
(15-1)/(1-0)=15
(34-15)/(2-1)=19
(48-34)/(3-1)=14
(60-48)/(4-3)=12
(62-60)/(5-4)=2
13
Law of Diminishing Returns
• The law of diminishing returns states that
as a firm uses more of a variable input
without changing the quantity of fixed
inputs, the marginal product of the variable
input will eventually decline (because its
productivity will be affected by the lack of
the fixed input).
14
Law of Diminishing Returns
• For example: Consider a factory with 10 jean machines.
Suppose one machine can be used by one worker. The first
ten workers can each have a machine. The next few can
carry raw materials for those on the machines. However
eventually you get to a point where additional workers are
just standing around getting in each others way.
Eventually the MP of each additional hour worked will
decline due to the bottleneck in the number of machines.
• The law of diminishing returns is the reason why TP, AP
and MP curves rise reach a max and then fall.
15
Fixed & Variable Costs
• A fixed cost is one that does not change with the
volume of output produced. (Ex: The rent on your
factory space stays the same regardless of how
many jars of Salsa you produce)
• A variable cost is one that depends upon the
volume of output produced. (Ex: The more Salsa
you make the more you spend on raw materials
like spices, tomatoes etc.)
16
Costs & Salsa
Factors Employed Factor Remuneration
Type of Cost
Land
Labor
Capital
Raw Materials
Fixed
Variable
Fixed
Variable
Rent
Wages
Rent
Raw Material Costs
TFC = Rent on Land + Rent on Machines
TVC = Wages + Raw Material Costs
TC = TFC + TVC
17
TFC, TVC & TC
TFC ($) TVC ($)
60
0
60
30
60
40
60
45
60
55
60
75
60
120
TC ($)
60
90
100
105
115
135
180
200
180
160
140
COSTS
Q
0
1
2
3
4
5
6
120
100
80
60
40
20
0
0
2
4
6
8
QUANTITY
TC = TFC + TVC
18
Output
Output on the Y -Axis
7
6
5
4
3
2
1
0
TFC
TVC
TC
0
25
50
75 100 125 150 175 200
Costs
19
TFC, TVC & TC Curves
• TFC is a horizontal line because fixed costs
do not change with the quantity produced.
(Rent for the factory does not change with
how much Salsa you make)
• TVC has an inverse S shape because of the
law of diminishing marginal product.
• TC is parallel to TVC and is higher than
TVC by the amount of TFC.
20
Marginal Cost
• Marginal cost is the change in total cost
resulting from a one unit increase in output.
Output
0
Q1 (10)
Q2 (30)
TC
0
TC1 ($20)
TC2 ($40)
MC= (TC2 - TC1)/(Q2 - Q1)
(20-0)/(10-0) = $2
(40-20)/(30-10)= $1
21
Points to note about MC
• MC is independent of fixed costs. A change
in fixed costs (like rent) will not change
MC. (except for the first unit)
• MC = (TC2 – TC1)/(Q2 – Q1)
= (TFC2 + TVC2 – TFC1 – TVC1)/(Q2 – Q1)
= (TVC2 – TVC1)/(Q2 – Q1)
Q TFC($) TVC($)
0
60
0
1
60
30
2
60
40
3
60
45
4
60
55
5
60
75
6
60
120
TC($)
60
90
100
105
115
135
180
22
Points to note about MC
• MC is obtained by plotting the slope of TC
at each point against quantity (Q).
• Total fixed cost (TFC) gets absorbed into
the MC of the first unit and does not affect
MC after that.
• MC is U-shaped because of the law of
diminishing marginal product.
23
Average Costs AC, AFC & AVC
• The average cost of production is defined as
the total cost divided by the number of units
of output.
• AC = TC/Q = (TFC + TVC)/Q
= TFC/Q + TVC/Q = AFC +AVC
24
Points to note about Average
Costs
• AFC is downward sloping because as more
units get produced the fixed costs get spread
out over a larger volume resulting in lower
and lower AFC. (A rent bill of $500 spread
out over a 100 bottles of salsa is an AFC of
$5, but the same rent amount of $500 spread
out over 500 bottles of salsa is just $1)
25
Points to note about Average Costs
• AVC is U – shaped because of the law of
diminishing MP.
– As more labor is hired the MP of labor rises (jars of
salsa produced per hour go up). Now as workers are
producing more and more per hour at the same wage
the variable cost per jar is going down. ( For example a
worker making $10 an hour that produces 50 jars
implies a labor cost of $1/5 of a dollar. If he/she
produces more jars per hour the labor cost per jar will
fall.
– As more labor is hired eventually MP declines and the
variable costs due to the variable input (labor) per jar
will go up.
– Thus AVC declines reaches a minimum and then rises
26
as Q increases.
Points to note about Average Costs
• AC is U-shaped. It falls at first as Q
increases due to a falling AFC and a falling
AVC. Then the rising AVC outweighs the
falling AFC and AC rises. The AC has a ushape in part due to the shape of AFC and in
part due to the shape of AVC.
27
Points to note about Average Costs
• AC is derived by plotting the slope of the
ray from the origin to each point on the TC
curve against the Quantity Q at that point.
• A rise (fall) in TFC or TVC shifts TC up
(down) and thus also shifts AC up (down)
28
Summary of SR Average &
Marginal Cost Curves
• MC cuts ATC and AVC at their minimum points.
• MC is u-shaped
• MC lies below ATC & AVC when they are falling
and above ATC & AVC when they are rising
• Changes in FC shift AC but not AVC & MC.
Changes in variable costs shift AVC & MC but not
AFC
• AC & AVC are u-shaped
29
Long run Average Cost
• The LRAC is the locus of points denoting the least
average cost of producing a given output level
from all available plant sizes.
• LRAC is the lower envelope of the SRAC curves.
• LRAC is U-shaped because of the laws of returns
to scale (RTS)
30
Long run Average Cost:
• Increasing RTS:
As all inputs are increased by some proportion
alpha (say 10%) output increases by more than
that proportion (i.e. more than 10%)
• Decreasing RTS:
As all inputs are increased by some proportion
alpha (say 10%) output increases by less than that
proportion (i.e. less than 10%)
31
Long run Average Cost:
• Constant RTS:
As all inputs are increased by some proportion
alpha (say 10%) output increases by exactly that
proportion (i.e. 10%)
• Economists claim that the falling part of LRAC is
due to IRS and finally when a firm gets too big
and DRS set in, the LRAC starts to rise.
32