Managerial EconomicsTheory and Estimation of

ProductionAalto University

School of ScienceDepartment of Industrial Engineering and

ManagementJanuary 12 – 28, 2016

Dr. Arto Kovanen, Ph.D.Visiting Lecturer

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 …

What is a firm?

It is about profits …

Mankiw, Principles of Economics

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

What is the objective of a firm?

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

Profit maximization

A firm typically has economic objectives such as 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

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

Other goals for the firm (cont.)

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

Business vs. financial risk

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-of-pocket, costs as well as implicit costs (value of inputs used in the production for which no direct payments are made)

Alternative measures of profits

Economic vs. accounting profits

Mankiw, Principles of Economics

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 ?

Alternative measures of profits (cont.)

How much to produce and what inputs to use? Production function and substitution between

inputs is important to understand Production in the short run

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

Firm’s production decisions

How do we explain production?

Labor

Capital

Productivity

Physical

Human

Technology

Institutions

Fact

ors

of

Prod

ucti

onProduction function

Y = A F(K,L)

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 (cont.)

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

Production in the short run (example)

Units of Y Employed

8 37 60 83 96 107 117 127 1287 42 64 78 90 101 110 119 1206 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 954 24 39 52 60 67 73 79 853 17 29 41 52 58 64 69 732 8 18 29 39 47 52 56 521 4 8 14 20 27 24 21 17

1 2 3 4 5 6 7 8Units of X Employed

Output Quantity (Q)

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

Labor Unit (X)

Total Product

(Q or TP)

Average Product

(AP)

Marginal Product (MP)

Total Revenue Product (TRP)

Marginal Revenue Product (MRP)

Total Labor Cost

(TLC)

Marginal Labor Cost

(MLC)TRP-TLC

MRP-MLC

0 0 0 0 01 10,000 10,000 10,000 20,000 20,000 10,000 10,000 10,000 10,0002 25,000 12,500 15,000 50,000 30,000 20,000 10,000 30,000 20,0003 45,000 15,000 20,000 90,000 40,000 30,000 10,000 60,000 30,0004 60,000 15,000 15,000 120,000 30,000 40,000 10,000 80,000 20,0005 70,000 14,000 10,000 140,000 20,000 50,000 10,000 90,000 10,0006 75,000 12,500 5,000 150,000 10,000 60,000 10,000 90,000 07 78,000 11,143 3,000 156,000 6,000 70,000 10,000 86,000 -4,0008 80,000 10,000 2,000 160,000 4,000 80,000 10,000 80,000 -6,000

Production in the short run (example)

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

Production in the long run

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 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?

Forms of production functions

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 function

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 right-hand 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 asLnC(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)

Estimating production (cont.)

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 estimatelog Q = c + α*log L + β*log K + ε

Total factor productivity

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: Human capital: education, training Knowledge spillovers, research and

development Institutions and government (legal and political

systems) Infrastructure

Total factor productivity (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

Drives of TFP

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 function and managerial decisions

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 voice-messaging system to the cost savings arising from the elimination of certain support personnel

Production (cont.)

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

Pro-growth policies

“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”

Growth regressions