Managerial Economics: Applying the Tools Topic 6, Part 2

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Managerial Economics Applying the ToolsTopic
6, Part 2

• Choosing output in a Monopoly
• Marginal Revenue and Marginal Cost
• Elasticity
• Paul Kerin Sam Wylie
• MBS Term 3, 2004

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Numerical Example

• 1,000 potential buyers (only interested in a
  single unit each). Have different WTP ranging
  from 0 to 1,000
• Monopoly seller with marginal cost of 200 per
  unit. Can supply entire market
• (Marginal cost cost of the last unit)
• ? if you are supplying 100 units, its the
  additional cost of supplying 100 instead of 99
• In this ex, each unit costs 200 ? MC 200

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Market Demand Curve

• 
  QD
• In simple algebra demand (QD) is QD 1000 - P

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Key question What quantity do you choose?

• You have a monopoly in this market
• ? no competition
• Can you choose to sell 800 units at a price of
  700?
• NO. You can sell 800 units at 200
• Or you can price at 700, and sell 300 units
• You can choose price OR quantity, but not both!
• Were going to looking at quantity choice, for
  reasons that will become clear

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One price fits all!

• (For now) assume you have to charge the same
  price to everyone
• As monopolist increases quantity
• the number of units sold increases (more buyers
  are included, more surplus is created)
• BUT the mark-up on each unit s/he does sell
  decreases.
• This is the monopolists dilemma. By increasing
  output the s/he can sell to more people, but
  captures less value from each of them

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Restricting supply

• Motive for restricting supply, under bargaining
• reducing the bargaining power of buyers
• Traditional motive for restricting supply, under
  posted pricing
• capturing more value from buyers with high WTP

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Output and Revenue
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Marginal Thinking

• Marginal thinking is very powerful. Its the
  right way to approach any decision that
• you can make in small increments
• each increment brings less benefit
• Look at the last increment is it worth it?
• Should I study 8 or 9 hours, today?
• Marginal thinking, for the monopolist
• Should I produce one more unit?

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Class exercise Marginal Revenue

• Suppose that a monopolist is currently not
  producing.
• What is the marginal revenue from producing 1
  unit? ( going from 0 to 1 units)
• What is the marginal revenue from producing 2
  units?
• What is the marginal revenue from producing 3
  units?
• ? Extrapolate
• What is the marginal revenue from producing 20
  units?

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What is the right stopping rule?

• Each additional unit you produce gives you less
  increase in revenue.
• But each additional unit costs 200
• each additional unit increases your costs by
  200.
• Your Marginal Cost is 200
• If you earn more than 200 in revenue from
  increasing output, do it!
• If you earn less than 200 in revenue from
  increasing output, dont!
• ? If marginal revenue is falling steadily, stop
  when Marginal Revenue is 200

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A Snapshot
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Graphically
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Maximising Profit

• When should monopolist supply an additional unit?
• Whenever the marginal profit (the extra profits
  from producing the final unit) is positive
• ? Produce until marginal profit falls to zero
• Marginal Profit
• (Revenue from another unit) - (cost of
  another unit)
• Marginal Revenue -
  Marginal Cost 0
• ? Produces up to the point where MR MC

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Maximising Profit

• Increase quantity until an increment brings you
  no extra profit, and youre at the maximum!
• P
• 
  Profits
• Q
  Q
• Marginal profit 0 at Q

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Calculus helps explain this (but you do not need
to use any calculus in this course!)

• Demand QD 1000 - P
• ? rewrite price in terms of Q P 1000 - Q
• Total Revenue P Q 1000Q - Q 2
• ? Marginal Revenue ?TR/?Q 1000 2Q
• Costs
• Total Costs 200Q
• ? Marginal Cost ?TC/?Q 200

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Marginal Condition

• Marginal Revenue equals Marginal Cost at the
  ideal output, Q
• 1000 - 2Q 200
• or
• Q 400
• Find ideal price by substituting Q into the
  inverse of the demand function
• P 1000 Q 600.

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In-class exercise

• Same demand curve as before, but now the cost of
  production is increasing
• Total Cost 200Q Q2.
• What is the cost of producing 30 units? 31 units?
  What is the marginal cost of the 31st unit?
• Calculate Marginal Cost, using derivatives. Is
  your answer for the marginal cost of the 31st
  unit approximately correct?
• How much does the monopolist choose to produce?
• Now suppose that you can sell as much as you want
  to on the US market, for 900 apiece, but demand
  in the Australian market is (1000 P). What do
  you do?

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Why split profits into MR and MC?

• Marginal Revenue and Marginal Cost are powerful
  tools, beyond the case of one factory producing
  for one market
• If Im selling in two markets
• Equalise Marginal Revenue in the two markets.
• Why? Imagine I was selling a fixed quantity (say
  180)
• If MR is higher in Australia, I can do better by
  moving one unit from the US, and selling it in
  Australia that gradually pushes MR down in
  Australia
• Now choose quantity set MR MC
• Double-check that you want to sell in both
  markets!

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Equalising Marginal Revenue in 2 markets
Carefully specify quantities!

• Let QA quantity sold in Australia
• And QTOT total quantity sold worldwide.
• Be careful which of those quantities you refer
  to!
• ---------------------------------------
• Suppose you have 2 factories, one in Melbourne
  and one in Geelong
• Total Cost in Factory M 200QM
• Total Cost in Factory G 150QG QG2
• And you can only sell in Australia. How much do
  you produce in each factory?
• How about if the total cost in Factory G 300QG
  QG2?

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Zero Marginal Cost

• A number of goods have Marginal Cost that is
  virtually zero anything downloaded off the
  internet, software, CDs,.
• How much should you sell, in these markets?
• Rule Increase output until MR MC
• ? Increase output until MR 0
• It turns out we can use a measure called
  elasticity to find the ideal output increase
  output until elasticity 1
• Elasticity is a measure of the sensitivity of
  demand to changes in price
• CAREFUL We are back to thinking about prices!

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Perfectly Elastic Demand
Price
Demand
Quantity
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Perfectly Inelastic Demand
Price
Demand
Quantity
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Elasticity and profit-maximisation

• In determining quantity price, it is important
  to know how sensitive demand is to price changes
• If it is relatively insensitive, then by raising
  price the monopolist does not exclude many buyers
• If it is relatively sensitive, raising price can
  exclude many buyers
• Price will be higher in a market where demand is
  more inelastic
• In our example The Australian market was more
  inelastic than the US market
• Price was higher in Australia

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Algebra underlying elasticity

• In mathematical terms, sensitivity of a demand or
  supply function is captured by the term
  elasticity
• For example, price elasticity of demand is the
  percentage change in quantity demanded divided by
  the percentage change in price

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Some Properties of Elasticity

• Its a negative number e.g., a 10 increase in
  the price of oil decreases quantity demanded by
  20. Therefore, ED -2
• Unit-Free Measure can compare elasticities among
  different goods. Is oil more price sensitive than
  butter?
• Elasticity vs. Slope these are not the same
  thing. Slope is ?P/?Q.

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Some Terminology
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Estimated Price Elasticities
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Explaining Elasticity Differences

• Degree of Substitutability
• Temporary vs. Permanent Price Changes
• Long-run vs. Short-run elasticity

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Elasticity as a Measure of Monopoly Power

• Recall that demand will be more elastic if close
  substitutes for a product exist.
• ? elasticity can be a measure of monopoly power.
• In particular, economists look to own-price
  elasticity of demand and to cross-price
  elasticities of demand (how much demand for
  other goods goes up, when your price goes up) to
  define markets
• ----------------
• The total revenue test is a method of estimating
  the price elasticity of demand by observing the
  change in total revenue that results from a price
  change (all other things remaining the same)

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Elastic Demand, Revenue and Expenditure

• If demand is elastic, an increase in price
  results in an larger percentage decrease in the
  quantity demanded and total revenue and total
  expenditure decrease

ED gt 1 then
P
Q
TR
and
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Inelastic Demand, Revenue and Expenditure

• If demand is inelastic, an increase in price
  results in an smaller percentage decrease in the
  quantity demanded and total revenue and total
  expenditure increase

ED lt 1 then
P
TR
Q
and
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Unit Elasticity, Total Revenue, and Expenditure

• If demand is unit elastic, an increase in price
  results in an equal percentage decrease in the
  quantity demanded and total revenue and total
  expenditure remain constant

ED 1 then
P
Q
TR no change
and
? MR 0
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Linear (straight) demand

• Confusing bit
• If the demand curve is actually straight, the
  elasticity is different at different points on
  the line
• There is one point at which the line has unit
  elasticity
• Marginal Revenue is zero at the unit elastic
  point.
• If MC0, profits are maximised at the point where
  MR0
• If MC0, you want to produce at the unit elastic
  point

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LAST Checking that youre at the right
pricewhen Marginal Cost is constant

• In our first example Marginal Cost 200 per
  unit.
• Lets call that per-unit cost c (so c200)
• To maximise Total Profits P(Q)?Q - c?Q
• ? Set marginal profit to 0.

You do not need to know this derivationbut do
need to know the result over the page
?P
?Q
?P
?Q
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Checking that youre at the right pricewhen
Marginal Cost is constant

• Flipping that around, it becomes
• That tells you what your markup over unit cost
  should be
• If you know your elasticity around your current
  price, you can check whether youre at the right
  price.
• WARNING 1 This rule only applies to the
  situations with constant Marginal Cost.
• But it shows that elasticity sums up everything
  you need to know about the demand curve.
• WARNING 2 Elasticity changes along the demand
  curve
• ? this is not a shortcut to finding the optimal
  price in an exam question