The Firm and Its Costs Lecture 3
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Neoclassical Theory of the Firm
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1. Neoclassical Theory of the Firm
2. Boundaries of a firm
3. Advantages of a market
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Economies of scale – small relative to the market
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Natural monopoly – has large fixed costs, usually infrastructure
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Examples: Telephone, gas, electricity, and water
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The bigger the company, the more average costs fall
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Economies of scope – firm has cost efficiencies by producing multiple products
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Costs to produce both q 1 and q 2 is C(q 1, q 2)
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Economies of scope have the characteristic
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C(q 1, q 2) < C(q 1, 0) + C(0, q 2)
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Example 1: Software company has expertise in computer programming
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Example 2: Bakery has ovens to produce multiple products
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Example 3: Steel fabrication plant has a variety of machines to make metal products
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Measure:
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gain = C(q 1, 0) + C(0, q 2)- C(q 1, q 2)
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Sc = gain / C(q 1, q 2)
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If S c = 0, company has no economies of scope
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If S c > 0, company has economies of scope
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Example
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C(q c, q t) = 50 qc + 60 qt - 1.5 qc qt
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Company produces 20 cars and 10 trucks
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C(20, 0) = 50 (20) + 60 (0) - 1.5 (20)(0) = 1,000
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C(0, 10) = 50 (0) + 60 (10) - 1.5 (0)(10) = 600
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C(20, 10) = 50 (20) + 60 (10) - 1.5 (20)(10) = 1,000 + 600 - 300 = 1,300
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S c = (1,000 + 600 - 1,300 ) / 1,300 = 0.231
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A firm reduces risk by contracting to another supplier
4. Advantages of a firm
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If market costs are too high, then a firm produces internally
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Transaction costs
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Search for a supplier
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Transportation costs
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Monitor quality
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Bounded rationality - people have limits to skills, knowledge, etc.
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Whether a firm produces internally or not?
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Frequency - firm will use a market if it rarely uses a machine or service
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Uncertainty - the more uncertainty, the greater the transaction costs
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Asset specific - an asset's value depends on geography, physical characteristics, or specialized human capital
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Specialized assets are costly
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Examples: Petroleum pipelines or machines that make autoparts
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Firm may choose to produce if assets are very specific
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Forms of Business Organizations
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Sole Proprietorship - one person owns / operates business
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Business is dissolved when owner dies
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Most numerous business in the U.S.
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Farms, restaurants, hotels, grocery stores, etc.
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Partnership - two or more people own a business
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Accounting and law firms
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General Partnership - other partners are liable for the actions of any partner, such as stealing, fraud, etc.
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Creditors can go after other partners
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Example - a partner secretly applies for a bank loan, steals the money, and leaves the country
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Limited liability partnership - creditors cannot go after the personal assets of the partners
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Corporations
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Approximately 20% of businesses are corporations, and they dominate businesses activity
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Shareholders own the corporation through stock
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Corporate managers should
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Corporations
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1. Corporations separate ownership and control
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Stockholders elect board of directors
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One share equals one vote
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Board of directors appoint professional managers
2. Managers may not act in the stockholders' best interest
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Stockholders want company to maximize stock prices or profits
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Managers want high compensation and retirement packages
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Managers want job security
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Company could lose managers if salaries and compensation are not comparable
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Compensation could be tied to a corporation's stock value
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Example - GM dumped its shareholders during the 2008 Financial Crisis
3. Corporations could suffer from x-inefficiency
4. A corporation is extremely complex
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Corporate managers may use rule of thumb to set prices
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CEO wants a rate of return of 10%; his compensation is tied to the stock value
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R 0 = profits / K
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R 0 is rate of return
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K is value of capital
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profits = TR - TC
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Total revenue
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Total costs
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profits = P q - (TC / q) q
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profits = P q - AC q = (P - AC) q
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Substitute profits into rate of return
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R 0 = (P - AC) q / K
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Everything is known except for market price
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Solve for P
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P = K R 0 / q + AC
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Price is capital per unit plus average costs
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Companies could use a markup on costs
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markup = (P - MC) / MC
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Common for a company to markup merchandise by 100%, so markup = 1
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Thus, P = 2 MC
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Example: If a company buys a computer for $300 and uses a markup of 100%, then it charges $600
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Markup was popular before the rise of the big retailers like Walmart
5. Book claims corporate managers may not take risks
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Profit Maximization
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1. Profits
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Accounting profits = revenue - explicit costs - implicit costs
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explicit costs - external payment for utilities, wages, taxes, etc.
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implicit costs - internal adjustment
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Economic profits = revenue - explicit costs - all implicit costs
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Include opportunity costs
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Accounting profits > economic profits
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Competitive market drives economic profits to zero
2. Profit maximization
- Note – Usually use d for partial derivatives (2 or more variables) and d for one variable
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Definitions
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Marginal cost (MC) – change in cost if firm produces one more unit
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Marginal revenue (MR) – change in revenue if firm sells one more unit
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Marginal profit (MP) – change in profit if firm sells/produces one more unit
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Example 1
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Example 2
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Max. profit MR = MC
3. Review of the cost functions
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Cost functions
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Fixed Cost (FC) - firm pays a cost that does not change with the production level
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Bank loan for building
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Overhead
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Total Varible Cost (TVC) - firm pays and costs vary on production level, q
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Utilities
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Wages
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Materials
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Total Cost (TC)
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Average Fixed Cost (AFC)
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Average Variable Cost (AVC)
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Average Total Costs (ATC)
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Marginal Cost (MC)
Q |
FC |
TVC |
TC |
MC |
AFC |
AVC |
ATC |
0 |
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50 |
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1 |
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62 |
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2 |
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10 |
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3 |
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10 |
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4 |
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90 |
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5 |
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21 |
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Solve for unknown costs
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The MC, AFC, AVC, and ATC are not defined at production, Q = 0
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At production, Q = 0, the variable costs are zero, or VC = 0. Thus, FC is 50. Fill the column for FC with 50.
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Calculate the AFC by dividing FC by Q
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Calcuate the VC for Q = 1 and Q = 4.
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Calculate the ATC for Q = 3. Then calculate the TVC.
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Calculate the AVC for Q = 5. Then calculate the TVC.
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Calculate the TC for Q = 3 and 5.
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Calculate the TC for Q = 2 by adding TC fro Q = 1 with the MC.
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Calculate the MC by differencing the TC. Since production increases by one, we divided the change in costs by one.
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The remaining numbers should be easy to calculate.
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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
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R(q) = P q
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Competitive firm sets production level, so P = MC
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Only one production level, q c, gives a MC that equals market price
5. Firm’s supply function is q c=S i(P)
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Given market price, firm chooses to supply q c units to market
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S i is supply from firm i
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Example: Corn, P = $5 per bushel
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Corn farmer wants to sell it for $6
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Nobody buys it; competitors sell it for $5
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Corn farmer sells it for $4
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He sells the corn, but could have sold it for $5, losing $1 for each bushel
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Markets
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Economies of Scale
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1.
Long run
- is a period of time sufficient for the firm to alter all factors of production.
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Firms can enter and exit the industry
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Long run differs by industry
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Short run – firm has at least one fixed factor of production
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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
Long Run ATC |
Per-Unit Cost |
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Output |
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ATC 2 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
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2. Why unit costs differ in the long run
Long Run ATC |
Per-Unit Cost |
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Output |
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Economies of scale
- per-unit costs fall as output (plant size) expands
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Mass production - large amounts of capital and machines
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Division of labor – increase in labor productivity
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Management specialization - departments can specialize in finance, personnel, and marketing
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Research and development
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Marketing and advertising costs
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Implement technology
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"Spread overhead over volume"
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Examples
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Constant returns to scale
- per-unit costs are constant as plant size is changed
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Diseconomies of scale
- per-unit costs rises as output (plant size) expands
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Bureaucratic inefficiencies
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More difficult to coordinate workers
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Monitoring problems, such as workers shirking
3. Special cases
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Indivisibilities – production cannot be scaled down
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Example: A firm has to produce at least 2,500 metric tonnes of aspartame per year to be a low cost producer
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Aspartame – an artificial sugar use in diet sodas and drinks
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Canadian demand is 359 metric tonnes per year
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Not efficient to build an aspartame plant there
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Volumetric returns to scale - applies to containers and pipes
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Chemical container
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Volume is production
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Volume, V = pr 2h
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r is radius
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h is height
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Surface area
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Equation is below
4. Measure, S(q) = AC(q) / MC(q)
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S(q) > 1, Economies of scale
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S(q) = 1, Constant returns to scale
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S(q) < 1, Diseconomies of scale
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