Managerial Economics
Theory and Estimation of
Production
Aalto University
School of Science
Department of Industrial Engineering and Management
January 12 – 28, 2016
Dr. Arto Kovanen, Ph.D.
Visiting Lecturer
What is a firm?
 Firms or businesses should be viewed as entities that
transform productive resources (inputs) into outputs
that can be sold – it is a process!
 Primary produces, manufacturing, services, trade etc.
 The manner in which productive resources are brought
together and organized will depend on the organizing
objectives and principles of the operator/management
 What does it require?
 Various types of labor, other materials, production
process, decision-making …
It is about profits …
Mankiw, Principles of Economics
What is the objective of a firm?
 Economists typically assume that the goal of the firm is
to maximize its profits, subject to resource constraints
and market information and structures
 The horizon is not just the current period but it
includes also future periods (is it infinite?)
 Hence, it is assumed that the firm maximizes the
present, discounted value of the stream of profits
Profit maximization
 In this equation π = profits = total revenues – total
costs while i stands for the discount interest rate
 Decisions on revenues and costs are often made by
separate entities within the firm, such as
 The marketing department may be responsible for sales,
which impact total revenues
 The production department has the responsibility for the
firm’s cost of production
 Corporate finances are handled by another department,
to support capital investments, and hence has an interest
in the cost of capital (the discount rate)
 Coordination is important within the organization
Other goals for the firm
 A firm typically has economic objectives such as



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Gaining market share
Increasing return to investment
Improving customer satisfaction
Increasing shareholder value
 It may also have non-economic objectives such as
 Better workplace environment
 Improved product quality (this is related to customer
satisfaction)
 Servicing the community (a “good citizen”)
 Knowing firm’s goals is critical for effective decisions
Other goals for the firm (cont.)
 Argument: companies do not maximize profits but
instead their aim is to focus on
 Position and power of shareholders and management
 Shareholders are interested in the return to investment
 Managers may be concerned about job security or their
compensation (e.g., based on stock performance)
 But in the end companies must be profitable
 The stock price reflects company’s profitability over time
 If managers’ compensation is based on the stock price,
then it reflects the company’s profitability
Business vs. financial risk
 Firms face two types of risks:
 Business risk
 Financial risk
 Business risk involves variation in returns due to ups
and downs of the economy, the industry, and the firm
 All firms face business risk to a varying degree
 Financial risk concerns variations in the returns that are
induced by leverage (borrowing)
 The higher the degree of leverage, the greater the
potential for fluctuations in the earnings
Alternative measures of profits
 What do we mean by “profit”?
 Accounting profits, based on the books of the firm,
may not match the meaning of the term for
economists
 Economists’ notion of profit takes into account that
any resource is scarce and has alternative uses
 Costs in economic terms have to do with forgoing the
opportunity to produce alternative goods and services
 Economic costs include all relevant explicit, out-ofpocket, costs as well as implicit costs (value of inputs
used in the production for which no direct payments
are made)
Economic vs. accounting profits
Mankiw, Principles of Economics
Alternative measures of profits
(cont.)
 Example: Charles owns a small grocery store in a busy
street and earns $200,000 annually. His out-of-pocket
costs total $180,000, of which he pays $30,000annual
salary to himself. A supermarket chain wants to hire
Charles for $60,000 per year.
 Calculate accounting and economic profits for Charles?
 What is his opportunity cost of owning and managing
the grocery store?
Alternative measures of profits
(cont.)
 An important concept in economics is that of normal
profit, sometimes referred to as normal rate of return
 It is the level of profit required to keep a firm engaged
in a particular activity
 Alternatively, it represents the rate of return on the
next best alternative investment of equivalent risk
 Normal profit is a form of opportunity cost and hence
represents a component of total economic cost
 Normal profit, πN , equals TC – TCO where the last term
is total operating costs
Alternative measures of profits
(cont.)
 A firm breaks even in an economic sense (i.e., is
earning zero economic profit) when it is earning a rate
of return equal to the rate of return on best alternative
 That is, its operating profit, πO = TR – TCO
= TR - TC – πN
 Furthermore, economic profit, π = πO + πN
 When operating profits are positive, the firm is said to
be earning above-normal rate of return
 Example: A firm has an operating profit of $150,000. Its
total revenues were $200,000 and total economic costs
were $25,000. What is the company’s πN ?
Firm’s production decisions
 How much to produce and what inputs to use?
 Production function and substitution between inputs is
important to understand
 Production in the short run
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Total, average, and marginal product
Marginal rate of technical substitution between inputs
Law of diminishing returns
Different stages of production
Optimal use of variable inputs
 Production in the long run
 Return to scale
 All inputs are considered variable
How do we explain production?
Factors of
Production
Labor
Capital
Productivity
Production function
Y = A F(K,L)
Physical
Human
Technology
Institutions
Production (cont.)
 A production function defines the relationship
between inputs used in the production process and the
maximum amount of output that can be generated
within a given time period and with a given technology
 Mathematically, the production function can be
expressed as
Q = f(X1, X2, … …, Xk)
where Q is output and Xs are inputs (e.g., labor, capital,
energy, raw materials, other intermediate inputs, and so
on)
Production (cont.)
 Difference between short-run and long-run
 The short-run production function describes the
maximum amount of output that can be produced with
a given set of inputs, assuming that at least one of the
inputs is fixed (e.g., machinery and buildings)
 The long-run production function describes the
maximum amount of output that can be produced with
a given set of inputs, assuming that the firm is free to
adjust the level of all inputs
 What inputs can be adjusted in the short-run and what
inputs can be adjusted only over time?
Production in the short run
 Total product (TP) is another name for output in the
short run. The total production function is the same as
the short-run production function
 Marginal product (MP) of a variable input is the change
in output (or TP) resulting from a one unit change in
this input
 Average product (AP) of an input is the total product
divided by the level of the input, which measures the
level of output produced per unit of input
 Example: Q = f(X, Y) where X is variable input (labor)
and Y is fixed input (capital). Calculate MP and AP of X.
Production in the short run
(example)
Units of Y
Employed
8
7
6
5
4
3
2
1
37
42
37
31
24
17
8
4
1
60
64
52
47
39
29
18
8
2
Output Quantity (Q)
83 96 107 117 127
78 90 101 110 119
64 73 82 90 97
58 67 75 82 89
52 60 67 73 79
41 52 58 64 69
29 39 47 52 56
14 20 27 24 21
3
4
5
6
7
Units of X Employed
128
120
104
95
85
73
52
17
8
Production in the short run
 Based on these data, draw TP, MP, and AP curves for a
given level of the fixed input (Y)
 What can you say about the shape of TP, MP, and AP
curves?
 If MP is positive, what does it mean for TP?
 What is the value of MP when TP is at its maximum
level?
 What about the relationship between MP and AP?
When MP > AP, is AP rising or falling?
 The law of diminishing returns: what it is and illustrate
Production in the short run
 Three stages of production:
 Stage I: from zero units of variable input to where AP is
maximized (both AP and MP rising)
 Stage II: from the maximum AP to where MP = 0 (AP still
positive)
 Stage III: from where MP = 0 onwards (declining MP)
 Which stage should the firm operate?
 Why not operate in stage I where MP > 0?
 If the firm operates in stage II, how much it should
produce?
 How much the firm can sell and at what price to maximize
its profits (i.e., MR = MC of each input)
Production in the short run
(example)
Labor Total
Unit Product
(X) (Q or TP)
0
0
1
10,000
2
25,000
3
45,000
4
60,000
5
70,000
6
75,000
7
78,000
8
80,000
Average Marginal
Product Product
(AP)
(MP)
10,000
12,500
15,000
15,000
14,000
12,500
11,143
10,000
10,000
15,000
20,000
15,000
10,000
5,000
3,000
2,000
Total
Revenue
Product
(TRP)
0
20,000
50,000
90,000
120,000
140,000
150,000
156,000
160,000
Marginal
Revenue
Product
(MRP)
20,000
30,000
40,000
30,000
20,000
10,000
6,000
4,000
Total
Labor
Cost
(TLC)
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
Marginal
Labor
Cost TRP(MLC) TLC
0
10,000 10,000
10,000 30,000
10,000 60,000
10,000 80,000
10,000 90,000
10,000 90,000
10,000 86,000
10,000 80,000
MRPMLC
10,000
20,000
30,000
20,000
10,000
0
-4,000
-6,000
Production in the long run
 In the long run all inputs can be adjusted
 Return to scale describes what happens to the total
output when all inputs are changed by the same
amount (e.g., all inputs are doubled)
 As a result of the return to scale, total output can be
more than doubled (increasing returns to scale, IRTS),
exactly doubled (constant returns to scale, CRTS), or
increase less that the increase in the usage of inputs
(decreasing returns to scale, DRTS)
 Firm’s production function can exhibit initially IRTS,
then CRTS, and as output rises further, DRTS
Forms of production functions
 The basic form is given by (for 2 inputs)
Q = f(L, K) where L = labor and K = capital
 Substitutability between L and K
 Marginal return – increasing / decreasing?
 Some common forms:
 Constant Elasticity of Substitution (CES):
 Q = A[aL-c + (1-a)K-c]-1/c
where s = elasticity of substitution = 1/(1-c)
 If c = 1, L and K are perfect substitutes
 Cobb-Douglas: lnQ = ln(A) + aln(L) + (1-a)ln(K)
Forms of production functions
 If c approaches negative infinity, we get the Leontief
production function where inputs are perfect
complements (How does it look like?)
 Consider the following production functions:
 Q = 10*L – L2 +24*K – K2
 Q = 10*L0.6K0.4
 Q = 2*L + 4*K
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Calculate dQ/dL and dQ/dK, and dL/dK
Calculate Q/L and Q/K
Are MPL and MPK increasing or decreasing – show?
What is the relationship between L and K?
Given PL and PK of 5 and 15, where the firm produces?
Estimating production function
 Data for estimating production functions come from
a variety of sources
 Engineering data can provide answers to production
questions (e.g., how much output a machine yields)
 Production data records the amounts of inputs (labor,
capital, materials, etc.) and the resulting output that
can be specific for each plan, product type and so on
 Using production data the management can obtain
estimates showing the relationship between inputs
used in production and the resulting output (using
regression analysis)
 Provides a tangible representation of production
Estimating production (cont.)
 The Cobb-Douglas and CES production functions used
most commonly in empirical estimations (tractability)
 Estimation is usually done in log-linear form (parameter
estimates can be viewed as elasticities)
 That is, Q = ALaKb can be estimated in a linear form by
taking logarithms of the components:
log Q = log A + a*log L + b*log K + ε
 Because of logarithmic transformation, the parameters
a and b are now interpreted as elasticities (not slopes)
 We can test for a + b = 1 after running OLS
Estimating production (cont.)
 We need to ask if the error term is uncorrelated with
the variables on the right-hand side?
 Unknown sources of errors – no problem
 Observed variations in technology and the quality of
inputs, left-out factors of production (e.g., materials,
energy use, and land) not factored in the equation –
will create problems
 The latter lead to biased estimates since the righthand variables are not statistically independent of the
error term (some component of it)
Estimating production (cont.)
 Is there a way to overcome these problems?
 E.g., output of corn, C(t), depends on area planted,
K(t), and the number of sunny days, S(t)
 Production is given by the following linear form
Ln C(t) = a*lnK(t) + (1-a)*lnS(t)
 If we do not have data on “sunny days”, we estimate
the production function as
LnC(t) = a*lnK(t) + ε(t)
Estimating production (cont.)
where ε(t) = (1-a)lnS(t)
 If the farmer does not observe S(t) before choosing
K(t), then OLS would result in an unbiased estimate of
“a”
 If production also depends on the quality of land,
Q(t), which the farmer observes, but the estimation
does not, leaving it out will bias the estimate of “a”
 That is, the quality of land affects the farmer’s
decision on how large area of land he will farm
 Estimate factor demand function, which is a function
of market-determined prices not correlated with the
residual (alternative to production function)
Total factor productivity
 The term A (or log A) in the Cobb-Douglas production
function is an important parameter
 It is called Total Factor Productivity (TFP)
 It cannot be estimated directly, but instead is treated
as a residual, which account for effects in total output
not caused by identified inputs (often called Solomon
residual)
 Technological improvements and efficiency are two of
the biggest factors determining TFP
 In a regression analysis, one would estimate
log Q = c + α*log L + β*log K + ε
Total factor productivity (TFP)
 The constant term c can be interpreted as the rate of
technological change
 Because of technological change, productivity growth
can continue (e.g., return to capital has not declined in
rich countries)
 Other factors are important:
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

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Human capital: education, training
Knowledge spillovers, research and development
Institutions and government (legal and political systems)
Infrastructure
Drives of TFP
A firm can improve its TFP through a mix of:
 Technical change and innovation (frontier shift)
• Better techniques are brought into existence, through radical
innovation
• Existing techniques are brought to new records of productivity
• Less sophisticated techniques are discarded
 Catching up term (changes in the distance from the frontier)
• Occurs through adaptation of well-established techniques or
imitation (straightforward incorporation)
• It is enough that the world frontier shifts for an immobile
country to lose efficiency
Production function and managerial
decisions
 An understanding of the basic concepts of
production provides a solid conceptual framework
for firm’s decisions involving the allocation of firm’s
resources in the short and long run
 A careful planning helps firms to use their resources
in a rational manner
 Good capacity planning depends on the quality of
the forecast for demand and setting production
adequately
Production (cont.)
 Managers must understand the marginal benefits and
costs of each decision involving the allocation of
scarce resources
 In real world, data on the marginal product of each
input may not be available
 The company can evaluate trade-offs between
different alternatives
 E.g., compare cost of installing a new voicemessaging system to the cost savings arising from the
elimination of certain support personnel
Pro-growth policies
 Policies supporting the proximate determinants
 R&D policies
 Human capital policies
 Policies supporting the more distant determinants
 At the macro level : business environment
 Macroeconomic framework: more stability means
higher TFP
 Investment: Cost of capital; Savings; Infrastructure
 Institutions
 Markets: Labor, financial and international markets
 At the micro level: informal sector, inequality trap
Growth regressions
 “I just ran two million regressions” (Sala-i-Martin)
 We can use regressions to assess impact of economic
factors and government policies on growth
  =  + 1x1 + 2x2 + … + nxn + 
•
 - vector of growth rates
•
x - vectors of explanatory variables
 This has problems of reduced form regressions—
invites “data mining”