The Firm and Its Costs
Lecture 3

 

Neoclassical Theory of the Firm

1. Neoclassical Theory of the Firm

  • A firm is a single entity

  • A firm maximizes profit

  • A firm has the following production function

Production Function of a firm

  • Isoquants – a production level with units of labor and capital

    • Firm may substitute between labor and capital

    • The goal is to produce at low cost

An Isoquant

  • Leontiff technology – a firm uses fixed proportions between labor and capital

    • Produces at the corner

    • One worker for every machine

Leontiff Production Function

2. Boundaries of a firm

  • A firm is a series of contracts between parties

    • Workers, managers, and suppliers have contracts

    • Explicit - contract is written, such a contracts with suppliers

    • Implicit - contract is not written, such as contract between manager and worker

  • Ronald Coase

    • Internal: Firm could produce product

    • External: Firm could contract out production (market)

    • Firm expands production until internal transaction costs equal external transaction costs

  • Example: The petroleum industry

    • Vertically integrated – firm produces products sequentially within a firm

Vertical Integration of Petroleum Industry

3. Advantages of a market

  1. Economies of scale – small relative to the market

    • Natural monopoly – has large fixed costs, usually infrastructure

    • Examples: Telephone, gas, electricity, and water

    • The bigger the company, the more average costs fall

Economies of scale

  1. Economies of scope – firm has cost efficiencies by producing multiple products

    • Costs to produce both q1 and q2 is C(q1, q2)

    • Economies of scope have the characteristic

    • C(q1, q2) < C(q1, 0) + C(0, q2)

    • Example 1: Software company has expertise in computer programming

    • Example 2: Bakery has ovens to produce multiple products

    • Example 3: Steel fabrication plant has a variety of machines to make metal products

    • Measure:

      • gain = C(q1, 0) + C(0, q2)- C(q1, q2)

      • Sc = gain / C(q1, q2)

      • If Sc = 0, company has no economies of scope

      • If Sc > 0, company has economies of scope

    • Example

      • C(qc, qt) = 50 qc + 60 qt - 1.5 qc qt

      • Company produces 20 cars and 10 trucks

      • C(20, 0) = 50 (20) + 60 (0) - 1.5 (20)(0) = 1,000

      • C(0, 10) = 50 (0) + 60 (10) - 1.5 (0)(10) = 600

      • C(20, 10) = 50 (20) + 60 (10) - 1.5 (20)(10) = 1,000 + 600 - 300 = 1,300

      • Sc = (1,000 + 600 - 1,300 ) / 1,300 = 0.231

  2. A firm reduces risk by contracting to another supplier

    • Outsourcing – firm sends part of production to another firm

      • Big trend in the U.S.

      • Call help lines in India and the Philippines

      • Company outsources programming to India, Russia, etc.

4. Advantages of a firm

  • If market costs are too high, then a firm produces internally

  • Transaction costs

    • Search for a supplier

    • Transportation costs

    • Monitor quality

  • Bounded rationality - people have limits to skills, knowledge, etc.

    • Firm cannot use a contract to cover all possibilities

  • Whether a firm produces internally or not?

    1. Frequency - firm will use a market if it rarely uses a machine or service

    2. Uncertainty - the more uncertainty, the greater the transaction costs

    3. Asset specific - an asset's value depends on geography, physical characteristics, or specialized human capital

      • Specialized assets are costly

      • Examples: Petroleum pipelines or machines that make autoparts

      • Firm may choose to produce if assets are very specific

 

Forms of Business Organizations

  1. Sole Proprietorship - one person owns / operates business

    • Business is dissolved when owner dies

    • Most numerous business in the U.S.

    • Farms, restaurants, hotels, grocery stores, etc.

  2. Partnership - two or more people own a business

    • Accounting and law firms

    • General Partnership - other partners are liable for the actions of any partner, such as stealing, fraud, etc.

      • Creditors can go after other partners

      • Example - a partner secretly applies for a bank loan, steals the money, and leaves the country

    • Limited liability partnership - creditors cannot go after the personal assets of the partners

  3. Corporations

    • Approximately 20% of businesses are corporations, and they dominate businesses activity

    • Shareholders own the corporation through stock

    • Corporate managers should

      • Maximize stock prices

      • Maximize the shareholders' wealth

      • Maximize a firm's value

 

Corporations

1. Corporations separate ownership and control

  • Stockholders elect board of directors

  • One share equals one vote

  • Board of directors appoint professional managers

2. Managers may not act in the stockholders' best interest

  • Stockholders want company to maximize stock prices or profits

  • Managers want high compensation and retirement packages

  • Managers want job security

  • Company could lose managers if salaries and compensation are not comparable

  • Compensation could be tied to a corporation's stock value

  • Example - GM dumped its shareholders during the 2008 Financial Crisis

3. Corporations could suffer from x-inefficiency

  • X-inefficiency - company does not produce at minimum costs

  • Gov. bureaucracies also suffer from x-inefficiency

4. A corporation is extremely complex

  • Corporate managers may use rule of thumb to set prices

  • CEO wants a rate of return of 10%; his compensation is tied to the stock value

    • R0 = profits / K

      • R0 is rate of return

      • K is value of capital

    • profits = TR - TC

      • Total revenue

      • Total costs

    • profits = P q - (TC / q) q

      • Market price, P

      • Company sells q units

      • Average costs equal TC / q

    • profits = P q - AC q = (P - AC) q

    • Substitute profits into rate of return

    • R0 = (P - AC) q / K

    • Everything is known except for market price

    • Solve for P

    • P = K R0 / q + AC

    • Price is capital per unit plus average costs

  • Companies could use a markup on costs

    • markup = (P - MC) / MC

      • Marginal costs

    • Common for a company to markup merchandise by 100%, so markup = 1

    • Thus, P = 2 MC

    • Example: If a company buys a computer for $300 and uses a markup of 100%, then it charges $600

    • Markup was popular before the rise of the big retailers like Walmart

5. Book claims corporate managers may not take risks

  • True in some cases, but Many financial institutions took massive risks before the 2008 Financial Crisis

  • Reasons

    • Stockholders revolt - shareholders can sell shares if they are displeased with management

      • Usually weak and rare

      • Example - a stockholders' revolt worked against the Disney Corporation

    • A poorly run corporation is taken over by another corporation

      • Anticipated takeover boosts stock prices

      • Speculators buy stock before the takeover

      • Takeovers have insider trading problems

      • Note - common for parent company to accumulate debt for the takeover

        • After the takeover, the debt is pushed onto the acquired company

        • Company implements cost reduction

        • Reduces salaries, reduces benefits, lowers pension plan, etc.

Profit Maximization

1. Profits

  1. Accounting profits = revenue - explicit costs - implicit costs

    • explicit costs - external payment for utilities, wages, taxes, etc.

    • implicit costs - internal adjustment

      • Accountants recognize depreciation expense

      • Accountant do not recognize opportunity costs

      • Opportunity costs

        • Entrepreneur has alternative choice such as earn a salary

        • Forgone interest - entrepreneur used savings to start business

        • Entrepreneur can rent out his capital, rental rate

  2. Economic profits = revenue - explicit costs - all implicit costs

    • Include opportunity costs

    • Accounting profits > economic profits

    • Competitive market drives economic profits to zero

      • Normal rate of return - companies earn an accounting profit

2. Profit maximization

  • Firms exist to maximize profits

  • Revenue function, R(q)

    1. Given a firm’s production level, q, they get R revenue

    2. Depends on consumers' demand and market structure

  • Cost function, C(q)

    1. Given a firm’s production level, q, they pay C costs

  • Profit function

Equation 1

  • Note – Usually use d for partial derivatives (2 or more variables) and d for one variable

Equation 2

  1. Definitions

    • Marginal cost (MC) – change in cost if firm produces one more unit

    • Marginal revenue (MR) – change in revenue if firm sells one more unit

    • Marginal profit (MP) – change in profit if firm sells/produces one more unit

  2. Example 1

    • If MC = $5 and MR = $6, should firm produce one more unit?

    • MP = MR –MC = $6 - $5 =$1

    • Yes, increase production

  3. Example 2

    • If MC = $10 and MR = $5, should firm produce one more unit?

    • MP = $5 - $10 = -$5

    • No, reduce production

  4. Max. profit MR = MC

    • Works for all market structures

3. Review of the cost functions

  • Cost functions

    • Fixed Cost (FC) - firm pays a cost that does not change with the production level

      • Bank loan for building

      • Overhead

    • Total Varible Cost (TVC) - firm pays and costs vary on production level, q

      • Utilities

      • Wages

      • Materials

    • Total Cost (TC)

    • Average Fixed Cost (AFC)

    • Average Variable Cost (AVC)

    • Average Total Costs (ATC)

    • Marginal Cost (MC)

Q FC TVC TC MC AFC AVC ATC
0     50        
1     62        
2       10      
3           10  
4     90        
5             21
  • Solve for unknown costs

    1. The MC, AFC, AVC, and ATC are not defined at production, Q = 0

    2. At production, Q = 0, the variable costs are zero, or VC = 0. Thus, FC is 50. Fill the column for FC with 50.

    3. Calculate the AFC by dividing FC by Q

    4. Calcuate the VC for Q = 1 and Q = 4.

    5. Calculate the ATC for Q = 3. Then calculate the TVC.

    6. Calculate the AVC for Q = 5. Then calculate the TVC.

    7. Calculate the TC for Q = 3 and 5.

    8. Calculate the TC for Q = 2 by adding TC fro Q = 1 with the MC.

    9. Calculate the MC by differencing the TC. Since production increases by one, we divided the change in costs by one.

    10. The remaining numbers should be easy to calculate.

  • Answers are in red

Q FC TVC TC MC AFC AVC ATC
0 50 0 50 - - - -
1 50 12 62 12 50 12 62
2 50 22 72 10 25 11 36
3 50 30 80 8 16.67 10 26.67
4 50 40 90 10 12.50 10 22.5
5 50 55 105 15 10 11 21

4. Perfect Competition – many firms in market; single firm cannot influence price

  1. R(q) = P q

    • R(q) is revenue for a firm

    • P is market price

    • q is production level for a firm

Equation 3

  1. Competitive firm sets production level, so P = MC

  2. Only one production level, qc, gives a MC that equals market price

5. Firm’s supply function is qc=Si(P)

  1. Given market price, firm chooses to supply qc units to market

  2. Si is supply from firm i

  3. Example: Corn, P = $5 per bushel

    • Corn farmer wants to sell it for $6

    • Nobody buys it; competitors sell it for $5

    • Corn farmer sells it for $4

    • He sells the corn, but could have sold it for $5, losing $1 for each bushel

  4. Markets

    • Demand – consumers

    • Supply – producers

    • Market supply – for each market, horizontally sum the firm’s supply

Market supply for a competitive market

  • Mathematically,

    Equation 4
    • n: Total number of firms in a market

  • Competitive firm

    • C(q) = VC(q) + FC

  • Average cost (AC) = C(q) / q

    • Costs per unit of production

    • Mathematically,

Equation 5

  • Firm’s profits

Equation 6

  • Profits are a rectangular box

    • P – AC(qC) is height of box

    • qC – 0 is width of box

  • Graphically,

Profits for a competitive firm

  • Competitive firm, P = MC(q)

  • Book – defines profits as quasi-rents

    • Rent – unfair advantage

    • Quasi – similar, almost

    • Example: monopolies can earn profits in the long run

 

Economies of Scale

1. Long run - is a period of time sufficient for the firm to alter all factors of production.

  • Firms can enter and exit the industry

  • Long run differs by industry

    • Examples: Long run for an automobile factory using lots of machines may be 7 years

    • The long run for an internet company may be 1 year

  • Short run – firm has at least one fixed factor of production

  • Long-Run ATC - shows the minimum average cost of producing each output level when a firm is able to vary all production resources, including factory size

    • Allow the firm to vary among 3 factory sizes: ATC1, ATC2, ATC3. Which factory size should the firm produce?

Long Run ATC
Per-Unit Cost
Long-run Average Total Costs
Output
Blue arrow

ATC2 will give the factory the lowest per unit costs in the long run. The firm will be able to recuperate all its total costs, when:

Market price (P*) > = minimum of long-run ATC

2. Why unit costs differ in the long run

Long Run ATC
Per-Unit Cost
Long-run Average Total Costs
Output
  • Economies of scale - per-unit costs fall as output (plant size) expands

    • Mass production - large amounts of capital and machines

    • Division of labor – increase in labor productivity

      • Workers' skills increase

      • Savings in setup cost

      • Substituting machines for labor

    • Management specialization - departments can specialize in finance, personnel, and marketing

    • Research and development

      • Research and development – cost to design new product

      • Example: New drug cost $300 million to get regulatory approval

    • Marketing and advertising costs

    • Implement technology

    • "Spread overhead over volume"

    • Examples

      • Automobile

      • Electricity

      • Natural gas

      • Telecommunications including internet services

      • Computer chips

  • Constant returns to scale - per-unit costs are constant as plant size is changed

    • Small firms can be just as efficient as large firms

      • Apparel

      • Food processing

      • Publishing

      • Lumber

      • Retailing

      • Wood products

  • Diseconomies of scale - per-unit costs rises as output (plant size) expands

    • Bureaucratic inefficiencies

    • More difficult to coordinate workers

    • Monitoring problems, such as workers shirking

3. Special cases

  1. Indivisibilities – production cannot be scaled down

    • Example: A firm has to produce at least 2,500 metric tonnes of aspartame per year to be a low cost producer

    • Aspartame – an artificial sugar use in diet sodas and drinks

    • Canadian demand is 359 metric tonnes per year

    • Not efficient to build an aspartame plant there

  2. Volumetric returns to scale - applies to containers and pipes

A cylinder

  • Chemical container

    • Volume is production

    • Volume, V = pr2h

    • r is radius

    • h is height

  • Surface area

    • Fixed cost of container

    • Surface Area, A = 2pr2 + 2prh

  • Equation is below

Production divided cost

  • Per-unit costs fall as h and r become large

4. Measure, S(q) = AC(q) / MC(q)

  • S(q) > 1, Economies of scale

    • A natural monopoly has a S(q) > 1 for all levels of production

  • S(q) = 1, Constant returns to scale

  • S(q) < 1, Diseconomies of scale

A firm's cost functions

 

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