Applied Microeconomics

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Applied Microeconomics

• Cost

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Outline

• Variable and Fixed cost
• Avoidable and unavoidable costs
• Average and marginal cost
• Efficient Scale
• Long and short-run costs
• Durable goods
• Experience curve and TQM

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Readings

• Perloff Chapter 7
• Kreps Chapters 8 and 10
• Zandt Chapter 4 and 8

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Breaking Down Costs

• In the previous lecture we derived the total cost
  function, TC(x)
• Total cost can be separated into variable cost,
  VC(x), and fixed cost, F
• Fixed cost can be separated into avoidable fixed
  cost FA and unavoidable fixed cost FU

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Variable Costs

• A cost is variable if it depends on quantity
  produced
• Examples paper costs for a publisher, flour
  costs for a baker, bottle costs for a wine-maker

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Fixed Costs

• A cost is fixed if it does not depend on the
  quantity produced
• Avoidable fixed costs are fixed costs that do not
  have to be paid if the firm shuts down
• Unavoidable or sunk fixed costs have to be paid
  even if the firm shuts down production
• The distinction between fixed and variable, and
  avoidable or unavoidable fixed costs depends on
  the time horizon as we will see

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Total, Variable, and Fixed Costs
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Sunk Costs

• What is wrong with the following statement
• One reasoning for choosing incineration over
  containment is that so much money has already
  been spent on pursuing the incineration option. 
  If we go with containment, that money will all
  have been wasted.

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Sunk Costs

• Sunk or unavoidable costs are cost that have
  already been incurred and cannot be undone
• Such costs should be ignored when making
  production decisions

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Sunk Costs Example

• Suppose a pharmaceutical company owns a piece of
  land that it can develop.
• The company has two subsequent decisions to make
  
• At time 0 Whether to sell the land for 0.7M or
  build an endostatin plant on it at a cost of
  0.9M
• At time 1 If it builds the plant, whether to
  shut it down, to operate at low capacity, or to
  operate at high capacity

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Sunk Costs Example

• The profits from the different outcomes are (in
  millions of dollars)
• Decision Revenue Cost Profit
• Sell land 0.7 0.0 0.7
• Build, shut down 0.0 0.9 -0.9
• Build, low output 2.0 3.0 -1.0
• Build, high output 3.0 4.1 -1.1
• Hence, at time 0, the company should sell the land

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Sunk Costs Example

• Suppose now that for some reason the decision to
  build the plant is made at time 0
• The payoffs to the different strategies at time 1
  are (in millions of euros)
• Decision Profits Gross of S. C. Net of S. C.
• Shut down 0.0 -0.9
• Low output -0.1 -1.0
• High output -0.2 -1.1
• Hence, the sunk cost does not affect the optimal
  decision at time 1 to shut down!

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Sunk Costs

• There are numerous instances where investors (and
  governments!) keep on investing in loss-making
  project just because they have already wasted a
  lot of money on them
• The tendency for people to let sunk costs affect
  their decisions is called the fallacy of sunk
  cost (or the Concorde fallacy or throwing good
  money after bad)

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The Mathematics of Costs

• The average cost per unit of output is
  AC(x)TC(x)/x
• The marginal cost is MC(x)TC(x) in if the cost
  function is differentiable
• If production can only be made in discrete
  quantities, the marginal cost function is
  MC(x)TC(x1)-TC(x)

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Total, Marginal, and Average Cost
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Total Cost and Marginal Cost

• The following relationship holds between marginal
  cost and total cost
• MC(x)TC(x)
• TC(x)0?x MC(s)dsF
• Hence, total variable cost at x is the area under
  the marginal cost curve and to the left of x

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Total, Variable, and Marginal Cost
AreaVC(4)
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Average and Marginal Cost Near Zero

• If there is a fixed cost (TC(0)gt0), then average
  cost explodes as x goes to zero
  limx?0TC(x)/xlimx?0F/x8
• If there is no fixed cost (TC(0)0), then average
  cost converges to MC(0) as production tends to
  zero limx?0TC(x)/xlimx?0(TC(x)-TC(0))/xMC(0)

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Average and Marginal Cost Near Zero
Fixed Cost
No Fixed Cost
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Relationship Between Marginal and Average Cost

• By taking the derivative of the average cost we
  obtain AC(x)TC(x)/x-TC(x)/x2
  (MC(x)-AC(x))/x
• Hence
• Average cost is increasing (decreasing) whenever
  marginal cost is higher (lower) than average cost
• If marginal cost crosses the average cost curve,
  this is occurs exactly at the quantity where
  average cost is minimized

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Efficient Scale

• The output at which the average cost is minimized
  is called the efficient scale of production x
• With a U-shaped average-cost curve it can be
  found where AC(x)0
• Recalling that the marginal cost crosses the
  average cost curve exactly at this point gives us
  a useful tool for finding this quantity solving
  MC(x)AC(x)

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Efficient Scale
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The Time Horizon of Production

• Suppose Boeing Corp. currently is producing
  three 747s per month at a total cost of 65M
• What would it cost to increase production to six
  747s per month?
• Depends on the time horizon
• Next month?
• In 12 months?

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The Time Horizon of Production

• Recall that the total cost function, TC(x), gave
  the minimum cost of producing x units using the
  available technology and the necessary inputs for
  this
• Implicit in our derivation of this function was
  that the quantity of all factors of production
  (inputs) could be chosen freely
• However, this assumption is not true in the short
  run

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The Short Run and Long Run

• The short run is defined as a time horizon such
  that the quantity of some of the firms factors
  of production are fixed
• The long run is defined as a time horizon such
  that the quantity of all factors of production
  are variable
• The time span of both concepts depends on the
  particular industry

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Example Long Run

• Suppose a firm want to produce xL units of
  output, that it has production function
  f(K,L)KL, and that the market prices of K and L
  are given by rltw respectively
• Solving minK,LKrLw subject to KLxL gives us
  KxL, L0, and the long-run total cost
  LTC(xL)xLr

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Example Short Run

• Suppose that capital is fixed at K xL, but that
  labor is flexible in the short run
• If the firm want to increase production to x in
  the short run, it solves minLxLrLw subject to
  xLL x
• Solving gives us KxL, Lx-xL, and the short-run
  total cost STC(x,xL)xLr(x-xL)w
• If the firm instead want to reduce production to
  x- in the short run, cost will be the same as in
  the long run STCS(x-,xL)xLr

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Example Short- and Long-Run Total Cost Functions
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Short- and Long-Run Total Costs Functions

• In theory, the following relationships hold for
  the short-run and long-run total cost functions
  (where xL is the status-quo level of production
  and x is the new level)
• LTC(x)STC(x,xL)
• LTC(xL)STC(xL,xL)

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Are the Two Relationships Realistic?

• Labor utilization can be increased temporarily by
  overtime instead of hiring
• Suppliers may be more likely to change prices
  over time
• Assumes the mix of inputs is such that cost is
  minimized at xL, but what if prices of inputs
  changes dramatically so that this is not true?
• In general, more information is needed about the
  firm to verify the assumptions

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Long-Run and Short-Run Average and Marginal Cost
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Multiproduct Firms

• When firms produce more than one output, concepts
  such as average cost are not well defined
• If production processes are independent, then
  each can be treated as a separate firm
• If this is not the case, we can have either
  economies of scope (cheaper to produce together)
  or diseconomies of scope (cheaper to produce
  separately)
• Empirical studies reveal that refineries, and car
  producers have economies of scope, and railroads
  diseconomies of scope in passanger and freight

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Durable Assets

• Some assets can be used more than one period
• Buildings and land
• Machines
• Human capital
• Goodwill
• Demand-side assets such as reputation
• In theory, look at the sum of discounted of cash
  flows
• Accountants use depreciation over time instead of
  change in cash-flow at purchase

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Know How

• Firms sometimes learn less costly ways of
  producing by experience learning by doing
• The experienced curve is a way of modeling this
• In this model total cost depends on current
  production x and the cumulative amount produced
  before the current period X, TC(X,x)
• Empirical support from computer chips with each
  doubling of cumulative output of EPROM chips,
  average cost falls by 22

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Conclusions

• Total cost can be separated in avoidable and
  unavoidable fixed cost, and variable cost
• Sunk costs should be ignored when making
  production decisions
• At the efficient scale average cost is minimized
  and marginal cost equals average cost
• Short-run total costs are generally equal to the
  long-run costs at the status quo level of
  production and higher at other levels