© 2010 Pearson Addison-Wesley The Firms and Theory of Production

© 2010 Pearson Addison-Wesley

The Firms and Theory of Production


The Firm and Its Economic Problem

A firm is an institution that hires factors of production and organizes them to produce and sell goods and services.

The Firm’s Goal

A firm’s goal is to maximize profit.

If the firm fails to maximize its profit, the firm is either eliminated or bought out by other firms seeking to maximize profit.


Accounting Profit

Accountants measure a firm’s profit to ensure that the firm pays the correct amount of tax and to show it investors how their funds are being used.

Profit equals total revenue minus total cost.

Accountants use Internal Revenue Service rules based on standards established by the Financial Accounting Standards Board to calculate a firm’s depreciation cost.



Economic Profit

Economists measure a firm’s profit to enable them to predict the firm’s decisions, and the goal of these decisions in to maximize economic profit.

Economic profit is equal to total revenue minus total cost, with total cost measured as the opportunity cost of production.



A Firm’s Opportunity Cost of Production

A firm’s opportunity cost of production is the value of the best alternative use of the resources that a firm uses in production.

A firm’s opportunity cost of production is the sum of the cost of using resources

Bought in the market

Owned by the firm

Supplied by the firm's owner



Types of Business Organization

There are three types of business organization:

Proprietorship

Partnership

Corporation

Information and Organization


Proprietorship

A proprietorship is a firm with a single owner who has unlimited liability, or legal responsibility for all debts incurred by the firm—up to an amount equal to the entire wealth of the owner.

The proprietor also makes management decisions and receives the firm’s profit.

Profits are taxed the same as the owner’s other income.



Partnership

A partnership is a firm with two or more owners who have unlimited liability.

Partners must agree on a management structure and how to divide up the profits.

Profits from partnerships are taxed as the personal income of the owners.



Corporation

A corporation is owned by one or more stockholders with limited liability, which means the owners who have legal liability only for the initial value of their investment.

The personal wealth of the stockholders is not at risk if the firm goes bankrupt.

The profit of corporations is taxed twice—once as a corporate tax on firm profits, and then again as income taxes paid by stockholders receiving their after-tax profits distributed as dividends.



Why Firms?

Firms coordinate production when they can do so more efficiently than a market.

Four key reasons might make firms more efficient. Firms can achieve

Lower transactions costs

Economies of scale

Economies of scope

Economies of team production

Markets and Firms


Transactions costs are the costs arising from finding someone with whom to do business, reaching agreement on the price and other aspects of the exchange, and ensuring that the terms of the agreement are fulfilled.

Economies of scale occur when the cost of producing a unit of a good falls as its output rate increases.

Economies of scope arise when a firm can use specialized inputs to produce a range of different goods at a lower cost than otherwise.

Economies of team production

Firms can engage in team production, in which the individuals specialize in mutually supporting tasks.

Markets and Firms


Production

The theory of the firm describes how a firm makes cost-minimizing production decisions and how the firm’s resulting cost varies with its output.

Production is a process in which firm transform its inputs (factor of production) to output


Production function

Q = F( K, L )

Function showing the highest output that a firm can produce for every specified combination of inputs.

Q= Total Product

K= Capital (Fixed factor of Production)

L=Labor (Variable factor of Production)


The Short Run versus the Long Run

short run Period of time in which quantities of one or more production factors cannot be changed.

long run Amount of time needed to make all production inputs variable.

fixed input Production factor that cannot be varied


PRODUCTION WITH ONE VARIABLE INPUT (LABOR)

Average and Marginal Products

● average product Output per unit of a particular input.

● marginal product Additional output produced as an input is increased by one unit.

Average product of labor = Output/labor input = q/L

Marginal product of labor = Change in output/change in labor input = Δq/ΔL


Production FunctionWith One Variable Input

Total Product

Marginal Product

Average Product

Production orOutput Elasticity

TP = Q = f(L)

MPL =TP L

APL =TP L

EL =MPL

APL


Production with One Variable Input

0 10 0 — —

1 10 10 10 10

2 10 30 15 20

3 10 60 20 30

4 10 80 20 20

5 10 95 19 15

6 10 108 18 13

7 10 112 16 4

8 10 112 14 0

9 10 108 12 4

10 10 100 10 8


TotalOutput (q)

Amountof Labor (L)

Amountof Capital (K)

AverageProduct (q/L)

MarginalProduct (∆q/∆L)



The Slopes of the Product Curve

The total product curve in (a) shows the output produced for different amounts of labor input.

The average and marginal products in (b) can be obtained (using the data in Table 6.1) from the total product curve.

At point A in (a), the marginal product is 20 because the tangent to the total product curve has a slope of 20.

At point B in (a) the average product of labor is 20, which is the slope of the line from the origin to B.

The average product of labor at point C in (a) is given by the slope of the line 0C.

Production with One Variable Input


The Law of Diminishing Returns

As additional units of a variable input are combined with a fixed input, after a point the additional output (marginal product) starts to diminish. This is the principle that after a point, the marginal product of a variable input declines.


The law of diminishing return

X

MP

Increasing Returns

Diminishing Returns Begins

MP


The law of variable proportions states that as the quantity of one factor is increased, keeping the other factors fixed, the marginal product of that factor will eventually decline. This means that upto the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative. Assumptions of Law. →Constant technology--- This law assumes that technology does not change throughout the operation of the law. →Fixed amount of some factors.—One factor of production has to be fixed for this law. → Possibility of varying factor proportions—This law assumes that variable factors can be --changed in the short run.


If MP > AP then AP is rising.

If MP < AP then AP is falling.

MP=AP when AP is maximized.


The three stages of production

Stage I: The range of increasing average product of the variable input.

From zero units of the variable input to where AP is maximized

Stage II: The range from the point of maximum AP of the variable to the point at which the MP of is zero.

From the maximum AP to where MP=0

Stage III: The range of negative marginal product of the variable input.

From where MP=0 and MP is negative.


In the short run, rational firms should only be operating in Stage II.

Why not Stage III?

Firm uses more variable inputs to produce less output

Why not Stage I?

Underutilizing fixed capacity

Can increase output per unit by increasing the amount of the variable input


The three stages of Production



What level of input usage within Stage II is best for the firm?

The answer depends upon how many units of output the firm can sell, the price of the product, and the monetary costs of employing the variable input.


Production With Two Variable Inputs

Isoquants show combinations of two inputs that can produce the same level of output.

Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped.


LABOR INPUT

PRODUCTION WITH TWO VARIABLE INPUTS

TABLE 6.4 Production with Two Variable Inputs

Capital Input

1 2 3 4 5

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 115

5 75 90 105 115 120

Isoquants

● isoquant Curve showing all possible combinations of inputs that yield the same output.



Isoquants

● isoquant map Graph combining a number of isoquants, used to describe a production function.

A set of isoquants, or isoquant map, describes the firm’s production function.

Output increases as we move from isoquant q1 (at which 55 units per year are produced at points such as A and D),

to isoquant q2 (75 units per year at points such as B) and

to isoquant q3 (90 units per year at points such as C and E).

Production with Two Variable Inputs(continued)

Figure 6.4


Marginal Rate of Technical Substitution

Marginal Rate of Technical Substitution: The absolute value of the slope of the iso-quant. It equals the ratio the marginal products of the two inputs. Slope of iso-quant indicates the quantity of one input that can be traded for another input, while keeping output constant.


Properties of Isoquants

Isoquants are negatively sloped

A higher Isoquants represent a larger output

No two isoquants intersect or touch each other

Isoquants are convex to the origin



Diminishing Marginal Returns

Diminishing Marginal Returns Holding the amount of capital fixed at a particular level—say 3, we can see that each additional unit of labor generates less and less additional output.

Production with Two Variable Inputs(continued)



Substitution Among Inputs

Like indifference curves, isoquants are downward sloping and convex. The slope of the isoquant at any point measures the marginal rate of technical substitution—the ability of the firm to replace capital with labor while maintaining the same level of output.

On isoquant q2, the MRTS falls from 2 to 1 to 2/3 to 1/3.

Marginal rate of technical substitution

● marginal rate of technical substitution (MRTS) Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant.

MRTS = − Change in capital input/change in labor input

= − ΔK/ΔL (for a fixed level of q)

(MP ) / (MP ) ( / ) MRTSK LL K



Production Functions—Two Special Cases

When the isoquants are straight lines, the MRTS is constant. Thus the rate at which capital and labor can be substituted for each other is the same no matter what level of inputs is being used.

Points A, B, and C represent three different capital-labor combinations that generate the same output q3.

Isoquants When Inputs Are Perfect Substitutes



Production Functions—Two Special Cases

When the isoquants are L-shaped, only one combination of labor and capital can be used to produce a given output (as at point A on isoquant q1, point B on isoquant q2, and point C on isoquant q3). Adding more labor alone does not increase output, nor does adding more capital alone.

The fixed-proportions production function describes situations in which methods of production are limited.

Fixed-Proportions Production Function

● fixed-proportions production function Production function with L-shaped isoquants, so that only one combination of labor and capital can be used to produce each level of output.


Optimal Combination of Inputs

Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

C wL rK

C wK L

r r

C Total Cost

( )w WageRateof Labor L

( )r Cost of Capital K


Isocost Lines

An isocost line is a line that identifies all the combinations of capital and labor, two factor inputs, that can be purchased at a given total cost.

The line intersects each axis at the quantity of that input that the firm could purchase if only that input were purchased.

The slope of an isocost line is (minus) the ratio of input prices, w/r, indicating the relative prices of inputs.


Least Costly Input Combination

A point of tangency between an isocost line and an isoquant show the least costly way of producing a given output level.

Alternatively, a point of tangency shows the maximum output attainable at a given cost as well as the minimum cost necessary to produce that output.


Interpreting the Tangency Points

Golden rule of cost minimization: a rule that says that to minimize cost, the firm should employ inputs in such a way that the marginal product per dollar spent is equal across all inputs

MPL/w = MPK/r


If the firm is not producing at a tangency point…

Whenever MPL/w > MPK/r, a firm can increase output without increasing production cost by shifting outlays from capital to labor.

Whenever MPL/w < MPK/r, a firm can increase output without increasing production cost by shifting outlays from labor to capital.


The Expansion Path

The expansion path is a curve formed by connecting the points of tangency between isocost lines and the highest respective attainable isoquants.


Isocost Lines and the Expansion Path [Figure 8.4]



Isocost Lines

AB C = $100, w = r = $10

A’B’ C = $140, w = r = $10

A’’B’’ C = $80, w = r = $10

AB* C = $100, w = $5, r = $10



MRTS = w/r


RETURNS TO SCALE

● returns to scale Rate at which output increases as inputs are increased proportionately.

● increasing returns to scale Situation in which output more than doubles when all inputs are doubled.

● constant returns to scale Situation in which output doubles when all inputs are doubled.

● decreasing returns to scale Situation in which output less than doubles when all inputs are doubled.



Effect of a Change in Input Prices


Returns to Scale

Constant Returns to

Scale

Increasing Returns to

Scale

Decreasing Returns to

Scale


RETURNS TO SCALE

When a firm’s production process exhibits constant returns to scale as shown by a movement along line 0A in part (a), the isoquants are equally spaced as output increases proportionally.

Returns to Scale

However, when there are increasing returns to scale as shown in (b), the isoquants move closer together as inputs are increased along the line.

Describing Returns to Scale


Empirical Production Functions

Cobb-Douglas Production Function

Q = AKaLb

Estimated using Natural Logarithms

ln Q = ln A + a ln K + b ln L


Estimation of Production FunctionsAggregate Production Functions

Many studies using Cobb-Douglas did not deal with individual firms, rather with aggregations of industries or an economy.

Gathering data for aggregate functions can be difficult.

•For an economy: GDP could be used

•For an industry: data from Census of Manufactures or production index from Federal Reserve Board

•For labor: data from Bureau of Labor Statistics


Useful properties

Several Useful Properties :

The Marginal Product of capital and the marginal Product of labor depend on both the quantity of capital and the quantity of labor used in production, as is often the case in the real world.

K and L are represents the output elasticity of labor and capital and the sum of these exponents gives the returns on scale.

a + b = 1 Constant return to scale

a + b > 1 Increasing return to scale

a + b <1 Decreasing return to scale


Importance of Production Functions in Managerial Decision Making

Production levels do not depend on how much a company wants to produce, but on how much its customers want to buy.

Capacity Planning: planning the amount of fixed inputs that will be used along with the variable inputs. Good capacity planning requires:

Accurate forecasts of demand

Effective communication between the production and marketing functions


Innovations and Global Competitiveness

Product Innovation

Process Innovation

Product Cycle Model

Just-In-Time Production System

Competitive Benchmarking

Computer-Aided Design (CAD)

Computer-Aided Manufacturing (CAM)

© 2010 Pearson Addison-Wesley . Slide 55

Theory of Cost and Estimation


The Nature of Costs

Explicit Costs

Accounting Costs

arise from transactions in which the firm purchases inputs or the services of inputs from other parties

Economic Costs

Implicit Costs

Explicit cost

Alternative or Opportunity Costs


Implicit Costs

costs associated with the use of the firm’s own resources and reflect the fact that these resources could be employed elsewhere

Sunk Costs


Short-Run Cost

Total fixed cost (TFC) – the cost incurred by the firm that does not depend on how much output it produces

Total variable cost (TVC) – the cost incurred by the firm that depends on how much output it produces


Total cost (TC) – the sum of total fixed and total variable cost at each output levelMarginal cost (MC) – the change in total cost that results from a one-unit change in outputAverage fixed cost (AFC) – total fixed cost divided by the amount of outputAverage variable cost (AVC) – total variable cost divided by the amount of outputAverage total cost (ATC) – total cost divided by the output


Short-Run Cost Functions

Total Cost = TC = f(Q)

Total Fixed Cost = TFC

Total Variable Cost = TVC

TC = TFC + TVC



Average Total Cost = ATC = TC/Q

Average Fixed Cost = AFC = TFC/Q

Average Variable Cost = AVC = TVC/Q

ATC = AFC + AVC

Marginal Cost = TC/Q = TVC/Q



Q TFC TVC TC AFC AVC ATC MC0 $60 $0 $60 - - - -1 60 20 80 $60 $20 $80 $202 60 30 90 30 15 45 103 60 45 105 20 15 35 154 60 80 140 15 20 35 355 60 135 195 12 27 39 55



Behind Cost Relationships

• The shape of the TVC curve is determined by the shape of the TP curve, which in turn reflects diminishing marginal returns.


Short-Run Cost Curves


The marginal product curve of the variable input generally rises and then falls, attributable to the law of diminishing marginal returns.

As a result, the MC curve will first fall and then rise

Marginal Cost


The average product curve rises, reaches a maximum, and then falls, due to the law of diminishing marginal productivity.

As a result, the AVC curve will fall and then rise.The AFC curve declines over the entire range of output as the amount of total fixed cost is spread over ever-larger rates of output.

The ATC curve is the sum of AFC and AVC. It measures the average unit cost of all inputs, both fixed and variable, and must also be U-shaped.

Average Cost


When marginal cost is below average (total or variable) cost, average cost will decline.When marginal cost is above average cost, average cost rises.When average cost is at a minimum, marginal cost is equal to average cost.

Marginal-Average Relationships


Geometry of Cost Curves


Long-Run Cost Curves


Economies of Scale and Diseconomies of Scale

Economies of scale – a situation in which a firm can increase its output more than proportionally to its total input cost

Diseconomies of scale – a situation in which a firm’s output increases less than proportionally to its total input cost


Long-Run Cost Curves

Long-Run Total Cost = LTC = f(Q)

Long-Run Average Cost = LAC = LTC/Q

Long-Run Marginal Cost = LMC = LTC/Q


Derivation of Long-Run Cost Curves


Relationship Between Long-Run and Short-Run Average Cost Curves


Possible Shapes ofthe LAC Curve


Cost-Volume-Profit Analysis

Total Revenue = TR = (P)(Q)

Total Cost = TC = TFC + (AVC)(Q)

Breakeven Volume TR = TC

(P)(Q) = TFC + (AVC)(Q)

QBE = TFC/(P - AVC)


Cost-Volume-Profit Analysis

P = 40

TFC = 200

AVC = 5

QBE = 40


Empirical Estimation

Functional Form for Short-Run Cost Functions

2 3TVC aQ bQ cQ

2TVCAVC a bQ cQ

Q

22 3MC a bQ cQ

Theoretical Form Linear Approximation

TVC a bQ

aAVC b

Q

MC b


Empirical Estimation

Theoretical Form Linear Approximation


Estimating Cost Functions

Techniques:

Surveys

Econometric specification

New entrant/survivor technique – method for determining the minimum efficient scale of production in an industry based on investigating the plant sizes either being built or used by firms in the industry


Minimizing Costs Internationally

Foreign Sourcing of Inputs

New International Economies of Scale

Immigration of Skilled Labor

Brain Drain

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© 2010 Pearson Addison-Wesley The Firms and Theory of Production