Theory of Production/Firm
Course Teacher: Dr. Abdur Rashid Sarker
Department of Economics The University of Rajshahi
Email: [email protected]
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Inputs and Production Functions Consumer Theory
Theory of the Firm
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Inputs and Production Functions
In this chapter we will cover:
Ownership and management of the firm
Inputs and production
Marginal Product (similar to marginal utility)
Average Product
Isoquants (similar to indifference curves)
Marginal rate of technical substitution (MRTS, similar to MRS)
Returns to scale
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Ownership and management of the firm
What is a firm?
A business firm is an organization/entity that converts inputs such as labor, materials, and capital into
outputs, the goods and services to be sold to consumers, other firms, or the government.
Example: U.S. Steel combines iron ore, machinery and labor to create steel
You can also cite numerous examples…………..
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Ownership and management of the firm
Three legal forms
Sole proprietorships
Firms are owned and run by a single individual.
Partnerships
Businesses are jointly owned and controlled by two or more people. The owners operate under a partnership agreement.
Corporations
Corporations are owned by shareholders in proportion
to the number of shares of the stock they hold.
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Inputs: Productive resources, such as labor and capital, that firms use to manufacture goods and services (also called factors of production)
Output: The amount of goods and services produced by the firm
Production: transforms inputs into outputs
Technology: determines the quantity of output possible for a given set of inputs.
Inputs and Production Functions
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Production function: tells us the
maximum possible output that can be attained by the firm for any given
quantity of inputs.
Q = f(L,K,M) Q = f(P,F,L,A)
Computer Chips = f
1(L,K,M)
Econ Mark = f
2(Intellect, Study, Bribe)
Production function
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Production and Utility Functions
•In Consumer Theory, consumption of GOODS lead to UTILITY:
U=f(………..)
•In Production Theory, use of INPUTS causes PRODUCTION:
Q=f(Labour, Capital, Technology)
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A technically efficient firm is attaining the maximum possible output from its
inputs (using whatever technology is appropriate)
A technically inefficient firm is
attaining less than the maximum possible output from its inputs (using whatever
technology is appropriate)
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production set : all points on or below the production function
Note: Capital refers to physical capital
,not financial capital/venture capital (the money
required to start or maintain production).
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Example: The Production Function and Technical Efficiency
Q = f(L)
L Q
•
•
•
C
D
B
Production Set
Inefficient point
Production Function
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Causes of technical inefficiency:
1) Shirking
- Workers don’t work as hard as they can -Can be due to laziness or a union
strategy
2) Strategic reasons for technical inefficiency -Poor production may get government
grants
-Low profits may prevent competition
3) Imperfect information on “best practices”
- inferior technology
Production Function (PF)
The production function is the backbone of the Theory of the Firm.
The production function can be displayed in a variety of ways:
1.Product curves---short run PF
2. Isoquants---Long run PF
Total product (TP)
Total product is the number of units of output produced.
Marginal Product (MP)
Marginal product is the additional output generated by additional input, ceteris paribus.
Average Product (AP)
The average product is the output per input, ceteris paribus The Law of Diminishing Returns
The law says that as Labor increases, ceteris paribus, output increases at a decreasing rate. The Law of
Diminishing Returns simply says that Marginal Product is decreasing.
Product curves
Illustrating TP, MP and AP
At low levels of labor use, output is increasing at an increasing rate so the TP curve is curved upward and MP is
increasing.
When the MP curve reaches its peak, the TP curve is at an inflection point. From here,
additional labor leads to increases in output, but at a decreasing rate
As more and more labor is used, TP
reaches its maximum point (where
marginal product is zero).
Product curves
Relationship between AP and MP curves
The MP curve intersects the AP curve at the maximum value of the AP curve
Whenever the marginal is greater than the average, the average must be rising and whenever the marginal is less than the average, the average must be falling.
Thus, the only time the two curves can meet is when the marginal equals the average.
The Law of Diminishing Returns does not say that we always have diminishing
returns for every level of labor use.
Instead, the law says that, eventually, diminishing returns will set in.
Product curves
Isoquants
: Long-run production functionThe isoquant displays the combinations of L and K that yield the same output.
Isoquants show only efficient production.
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L K
Q = 20
Q = 40
All combinations of (L,K) along the isoquant produce 40 units of output.
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Example: Iso= equal, quants= output
Isoquants
Isoquants: Properties
Isoquants have most of the same properties as indifference curves.
Main difference
An isoquant holds quantity constant, whereas an indifference curve holds utility constant
Quantities with isoquants have cardinal properties ( Q=12 is twice as much as an output of 6) while utilities with
indifference curves have only ordinal properties ( 12 utils are associated with more pleasure than 6 utils, but not
necessarily twice as much pleasure.
Isoquants: Four Properties
Property 1: The farther an isoquant is from the origin, the greater the level of output
Property 2: Isoquants do not cross
Property 3: Isoquants slopes downward Property 4: Isoquants must be thin
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1. Linear Production Function:
Q = aL + bK
MRTS constant
Constant returns to scale
Inputs are PERFECT SUBSTITUTES:
For example 10 CD’s are a perfect substitute for 1 DVD for storing data.
Special Production Functions
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Example: Linear Production Function
L K
Q = Q0
Q = Q1
0
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Example: 2 pieces of bread and 1 piece of cheese make a grilled cheese sandwich
Special Production Function
Bread 27
Cheese
2 4
Q = 1
Q = 2
0 1 2
Example: Fixed Proportion Production Function
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3. Cobb-Douglas Production Function:
Q = aL
K
if + > 1 then IRTS
if + = 1 then CRTS
if + < 1 then DRTS
smooth isoquants
MRTS varies along isoquants
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Example: Cobb-Douglas Production Function
L K
0
Q = 40 Q = 20
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Marginal rate of technical substitution
(labor for capital): measures the amount of K the firm the firm could give up in exchange for an additional L, in order to just be able to
produce the same output as before.
Marginal products and the MRTS are related:
MP
L/MP
K= -K/L = MRTS
L,K6.5 Marginal Rate of Technical
Substitution (MRS)
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The marginal rate of technical substitution, MRTS
L,Ktells us:
The amount capital can be decreased for every increase in labour, holding output constant
OR
The amount capital must be increased for every decrease in labour, holding output constant
-as we move down the isoquant, the slope decreases, decreasing the MRTS
L,K-this is diminishing marginal rate of technical substitution -as you focus more on one input, the other
input becomes more productive
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MRTS
L,K=4
K
L
•
• MRTSL,K =1/4
4
2
1
•
1 2 4
MRTS
L,K=1
Q=16
Ridge lines
The ridge lines OR and OL enclose the area of rational operation/
feasible region of operation
MRTS/TRS : More detail
•Measure of degree of substitutability
•The tradeoff between two inputs in production
•It tells us how many units of capital the firm can replace with an extra unit of labour.
•The amount by which capital input can be reduced while holding quantity produced constant when one more unit of labour input is used
•MRTS= -2 value says that one unit of labour can replace 2 units of capital to get the same output
MRTS/TRS : More detail
What is the MRTS for a general Cobb-Douglas production , Q = ALaKb
MPL = ? MPK= ?
MRTS=
MRTS has serious defect as a measure of the degree of
substitutability: it depends on the unit of a measurement of the factors.
A better measure of the ease of factor substitution is provided by the elasticity of substitution.
The Elasticity of Substitution
The elasticity of substitution is the percentage change in the K-L ratio divided by the percentage change in the MRTS:
For q = ALaKb , What is the elasticity of substitution?
The Elasticity of Substitution
The Elasticity of Substitution
Elasticity of Substitution (EOS) = 1
EOS is a pure number that measures the rate at which substitution takes place
Returns to scale
Returns to Scale
How much output changes if a firm increases all its inputs proportionately
It helps a firm to determine its scale or size in the long-run Increasing Returns to Scale (IRS)
If output rises more than in proportion to an equal percentage in all inputs
Cause
Greater specialization of L and K by building a single large plant
Use of advanced technology, specialized equipment
Division of labour
Returns to scale
Decreasing Returns to Scale (DRS)
If output rises less than in proportion to an equal percentage increase in all inputs
Cause
As the firm grows, returns to scale are
eventually exhausted. There are no more
returns to specialization
Returns to scale
Decreasing Returns to Scale (DRS)
Causes
If the firm continues to grow, the owner starts having difficulty managing everyone
Difficulty of organizing, coordinating and integrating activities An owner may be able to manage one plant well but may have trouble running two
Returns to scale
Constant Returns to Scale (CRS)
When all inputs are increased by a certain percentage, output increases by that same percentage
Causes
Indivisibility of fixed factors
Specialization and indivisibilities of capital
Varying Returns to Scale
Varying Returns to Scale
Which values of will be associated with different kinds of returns to scale ?
EQUILIBRIUM OF THE FIRM: CHOICE OF OPTIMAL COMBINATION OF FACTORS OF PRODUCTION
Isocost line
All the combinations of two inputs, such as capital and labor, that have the same total cost.
Isoquant and Isocost to understand production decisions
LEARNING OBJECTIVE
Using isoquants and isocosts to understand production and cost
LEARNING OBJECTIVE
Using isoquants and isocosts to understand production and cost
The firm is in
equilibrium when it maximizes its output
given its total cost outlay and the prices of the
factors, w and r.
We see that the
maximum level of output the firm can produce,
given the
cost constraint, is X2
defined by the tangency of the isocost line, and the highest isoquant.
LEARNING OBJECTIVE
Using isoquants and isocosts to understand production and cost
In this case we have a single isoquant (first figure) which
denotes the desired level of output, but we have a set of isocost curves (second figure)
The firm minimises its costs by employing the combination of K and L determined by the point of tangency of the X isoquant with the lowest isocost line
LEARNING OBJECTIVE
Using isoquants and isocosts to understand production and cost
Points below e are desirable because they show lower cost but are not attainable for output X. Points above e show higher costs.
Hence point e is the least-cost point, the
point denoting the least-cost combination of the factors K and L for producing X.
The Slope and Position of the Isocost Line
The Position of the Isocost Line
The position of the isocost line depends on the level of total cost.
As total cost increases from
$3,000 to $6,000 to $9,000 per week, the isocost line shifts outward.
For each isocost line shown, the rental price of ovens is
$1,000 per week, and the wage rate is $500 per week.
LEARNING OBJECTIVE
Using isoquants and isocosts to understand production and cost
Choosing the Cost-Minimizing Combination of Capital and Labor
Choosing Capital and Labor to Minimize Total Cost
Jill wants to produce 5,000 pizzas per week at the lowest total cost.
Point B is the lowest-cost combination of inputs shown in the graph, but this
combination of 1 oven and 4 workers will produce fewer than the 5,000 pizzas needed.
Points C and D are
combinations of ovens and workers that will produce 5,000 pizzas, but their total cost is $9,000.
The combination of 3 ovens and 6 workers at point A produces 5,000 pizzas at the lowest total cost of $6,000.
Using isoquants and isocosts to understand production and cost
Expansion path
The tangency points A, B, and C lie along the firm’s expansion path, which is a curve that shows the cost- minimizing combination of inputs for every level of output.
In the short run, when the quantity of machines is fixed, the firm can expand output from 75 bookcases per day to 100 bookcases per day at the lowest cost only by moving from point B to point D and increasing the number of workers from 60 to 110.
In the long run, when it can increase the quantity of machines it uses, the firm can move from point D to point C, thereby reducing its total costs of producing 100 bookcases per day from $4,250 to $4,000.
A curve that shows a firm’s cost-minimizing combination of inputs for every level of output
