Download Week 2 Section Notes

Final Exam Review
EWMBA 201A
Eva Vivalt
October 3, 2009
Final Exam Review
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Administrative Stuff
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Final Exam for both sections: Friday October 9th 6pm.
Practice questions available on bspace.
Pricing project due next Monday or Tuesday.
Prof. Vardy’s review before class on Monday and Tuesday.
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Final Exam Review
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Today’s Agenda
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Overview of major course topics (recommend you use this for
a review check-list)
Tips, focusing mostly on second half since you have
previously seen a review on the first half
A selection from problem set #5
Extra time for questions after section! (Old exams, thought
questions, anything….)
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The meat of the course
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Basic economic concepts
Tools for analysis
Producer’s costs
Producer’s decision-making/strategies
Long-run market supply
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The meat of the course
• Basic economic concepts:
– Pareto efficiency as the key criterion – econ
doesn’t care about distribution but efficiency
– Perfectly competitive market (conditions for)
– Arbitrage
– First and second fundamental theorem of welfare
– Demand curves, supply curves, movement along
them vs. movement of the curves, and Consumer
Surplus
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The meat of the course
• Tools for analysis (producer or consumer):
– Elasticity
– Decision trees
– Decision-making under risk: Risk neutrality, riskloving, risk-aversion
• The resulting value of information
• An example of what can happen without perfect
information: auctions
– Game theory (Nash equilibria, rationality, common
knowledge of rationality)
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The meat of the course
• Producer’s costs:
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Sunk costs
Opportunity costs
Total costs, Average total costs
Fixed costs
Variable costs, Average variable costs
Marginal costs
And how these all relate to each other in problems.
- Related: economies of scale/diseconomies of scale
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The meat of the course
• Producer’s decision-making/strategies
– Profit maximization (not revenue maximization)
under perfect competition and monopoly
– Price discrimination
• Long-run market supply
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Tip!
• Think to yourself: on which of the topics on
the previous slides could you be asked a
“problem” question? On which of the topics on
the previous slides could you be asked a
“theory” question?
– You know there will be a mix.
– You also know that sometimes a problem question
can have a “thought” component, so don’t classify
problems as something to know how to calculate
but not understand.
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Final Exam Review
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Quick Review of Costs
•
Different types of costs:
• TC = FC + VC
• FC = Costs that do not vary with quantity
• VC = Costs that do vary with quantity
• MC = cost of one additional unit of production = dTC/dQ
• AC = TC/Q
• Opportunity cost = value of next best opportunity
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What else could you be doing with your resources?
Sunk costs = costs already expended or non-recoverable
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Is the cost behind you on the decision tree?
Final Exam Review
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Quick Review of Pricing
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Perfectly competitive firm sets P=MC to maximize profits
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Since firms are price takers and can sell as many units as they choose at
price P, MR = P for any firm.
In short-run equilibrium (without entry) firms can be profitable, if
AC<MC. If AC=MC then economic profit = 0. If AC>MC then a firm
should shut down.
Monopolist sets MR=MC to maximize profits
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Find MR by taking derivative of TR=P(Q)*Q (or if you have a demand
curve of the type P=a-b*Q, remember that MR=a-2b*Q – but really,
just do the calculus).
Revenues are not maximized at the same production point as profits,
unless MC=0 (revenues are maximized where MR=0).
Monopolist therefore produce at an elastic point on the demand curve,
unless MC=0, in which case elasticity = -1.
Remember the steps to find a maximum/minimum from previous
slides!
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Quick Review of Price Discrimination
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Price discrimination allows monopolist to charge different
rates to different consumers.
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1st degree: charge each consumer its WTP
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Only meaningful for a monopoly (Why?)
If some kind of PD is profitable, it helps the monopolist vs. single price
benchmark.
Ambiguous effect on consumers (some customers previously “shut
out” of the market may get to consume).
Not seen very often in real life
3rd degree: sort customers based on some observable trait
where it’s legal to charge different prices (e.g.: student tickets
at movies)
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Quick Review of Price Discrimination
2nd degree PD and its relatives: allow customers to self select
(versioning, intertemporal PD, quantity discounts)
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Give customers the incentive to self-select by making their consumer
surplus greatest for the product type you want them to select.
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Tips for 2nd Degree PD Problems
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Set up strategies or a “menu of options” and methodically
calculate the prices which get customers to do what you want
them to do. Pick the option that maximizes profit.
Some options to try:
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2.
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3.
Sell one product, only to high valuation group.
Sell one product to everyone (note high valuation group will get rent).
Set up a 2nd degree PD scheme.
General rules for setting up 2nd degree PD scheme:
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2.
Always charge low WTP group its maximum WTP for low quality
product.
Make sure that high WTP group buys high quality product by giving
more than CS from choosing low quality product.
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Long Run vs. Short Run
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Short run
• There may be fixed costs; the number of firms is fixed.
• Set MR=MC; exit if P<min AVC
• May want to stay open if P<ATC
Long run
• No fixed costs, all costs are variable.
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In long run, P=MC=minAC.
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This is definitional; hence “long run” varies by industry.
Firms with AC<MC make positive economic profit  enter.
Firms with AC>MC make negative economic profit  exit.
Thought question: why do firms produce if they’re getting 0
profits?
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Long Run Equilibrium
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Long-run competitive equilibrium (Can refer to P&R, p. 284)
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All firms in industry are maximizing profit.
No firm has incentive to enter or exit.
Price of product equates Qs with Qd.
Occurs where economic profits = 0 and MC = minAC
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To get the minimum point on an AC curve, you have 2 options:
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Set MC=AC and solve (since they cross where AC is lowest).
Take dAC/dQ and solve for where this equals 0.
Final Exam Review
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Problem Set #5, Q2
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TC=400+q^2  MC=2q and AC=400/q + q
A) Perfectly competitive market, P=100. How many pencils
do you produce?
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Solution approach: set P=MC and solve for q.
100=2q  q=50, profit=$2100
B) Market demand: Q=50,000-200P. How many firms are in
the market in the short run?
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Solution approach: Find Q, since firms homogenous, we know total
firms in market = Q/q
Q=50,000-200(100)=30,000  Firms = 30,000/50 = 600.
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Problem Set #5, Q2 cont.
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C) What happens in the long run?
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We know from part A) that firms are making economic profit. In the
LR we expect firms to enter to the point where firms make zero profit.
Solution approach: find where P=minAC
Approach (1): set MC=AC: 2q=400/q + q  q*=20
MC=40 P*=40 Q*=50,000-200(40)=42,000
total number of firms=42,000/20=2100.
Approach (2): set dAC/dq=0: -400/q^2 + 1 =0  q^2 = 400
q*=20….
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Problem Set #5, Q2 cont.
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D) One plant with new technology (P=$40 from before)
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TCnew=200+qnew^2/2  MCnew=qnew and ACnew=200/qnew +
qnew/2
Solution approach: set P=MCnew and solve for qnew.
40=qnew  qnew=40, profit (for new firm)=$600.
qnew=40 = 2x20 = 2xqold  two old firms replaced.
New number of firms: 2100 (before) – 2 (displaced) + 1 (new) = 2099.
E) Patent, so now can use technology in multiple plants
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Solution approach: build just enough new plants to drive older plants
out of market.
Set AC=MC to minimize costs (lowest part of AC curve)  200/q +
q/2 = q  q*=20.
Number plants = 42,000/20 = 2100.
Profit (per plant) = (40)(20) – [200+400/2]=$400.
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Problem Set #5, Q3
• A) On peak days, we face demand P=1000-Q. TR=P(Q)*Q=1000Q-Q2 
MR=1000-2Q.
• Solution approach: set MR=MC and solve for Q.
• What are our costs? If we have already booked the plane, the $20,000 lease
cost is sunk (if not, it’s a fixed cost), and the operating cost of $30,000 per
round-trip flight is also sunk or fixed given that we’ve already decided to
make the flight (sunk if we’ve paid for it, fixed if not) (i.e. think of it like
the fuel is in the plane, we’re just deciding how much to charge
passengers).
• Analogy: if you need to rent a building for a production process, if you
only need to produce in one building it’s a fixed cost, if you’re deciding
how many buildings to produce in because you might need more room
depending on how much you want to produce, it’s a variable cost (varies
with quantity produced), and if you’ve already paid for the building it’s a
sunk cost.
• So our only marginal cost for flying an additional person is $40/person.
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Problem Set #5, Q3 cont.
• A) (cont.)  Setting MR = MC, 1000-2Q=40  Q=480.
Problem: the plane can only carry 300 people. So carry 300
people – it’s the best you can do. But at what price? You can
afford to lose some customers by raising the price: with
demand P=1000-Q, P=700.
• On off-peak days, we similarly get: P=400-Q  TR=400Q-Q2
 MR=400-2Q  MR = MC  400-2Q=40  Q=180 
P=220.
• B) This question asks us about whether we choose to
*operate* the flight. Thus, it presumes we’ve already decided
whether to *lease* it. The lease cost is a sunk cost, and now
we are only considering whether to operate it.
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Problem Set #5, Q3 cont.
• B) (cont.) Should we operate?
• Solution approach: compare TR and TC to get profit.
• Peak days: TR=700*300=210,000,
TC=30,000+40*300=42,000  Profit=168,000
• Off-peak days: TR= 220*180=39,600,
TC=30,000+40*180=37,200  Profit=2,400
 Operate on both kinds of days since positive
profits.
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Problem Set #5, Q3 cont.
• C) Again, let’s calculate profit, this time taking the cost of the
lease into consideration.
• You can solve this question by calculating profits for the whole
6 month period if you prefer; you’ll get the same answer by
looking at a 1 week period, though, since the weeks are
identical.
• You could also solve this question by calculating e.g. peak
days TR = 210,000, TC = 42,000+20,000, etc.
• But as a short cut we can simply write weekly operating
profit=2*168,000+4*2,400=345,600 (total revenue net of
operation costs), weekly TC of renting = 7*20,000 = 140,000
 total profit of $205,600. Either way!
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Problem Set #5, Q3 cont.
• D) We can make 600 roundtrips! Great! – But is there that
much demand?
• We know from part A) that with the demand for off-peak days,
we only want to sell 180 tickets on off-peak days.  Since
operating any one flight has an operating cost associated with
it, we want these 180 tickets to be on the same plane.
• We know from part A) that with the demand for peak days, we
want to sell 480 tickets on peak days. Our MR and MC stay
the same (TR=P(Q)*Q=1000Q-Q2  MR=1000-2Q, MC=40
($40/person))  we still want to sell 480 tickets, and what will
be their price, now that we *can* sell that many tickets?
Simply plug back into the demand: P=1000-480=520.
• Percent of capacity used would fall, but so what?
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Problem Set #5, Q3 cont.
• E) Solution approach: calculate profits for the new option (as
before) but also compare to the other option (not leasing the
second plane) because you want to make the decision that
*maximizes* profits.
• Now that the lease cost isn’t a sunk cost, let’s re-do our profit
calculations: Operating profit for a peak day was (480*520)(2*30,000+480*40)=170,400. Operating profit for a non-peak
day was 2,400.  Weekly operating profit is
2*170,400+4*2,400=350,400. Weekly lease cost:
2*7*20,000=280,000  Weekly total profit of 70,400.
• But wait! We had higher profits when we only operated one
plane (part C). Thus, only lease one plane.
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General exam tips
• Pay attention to how much each question is worth and
make sure you don’t accidentally skip over a sub-part
of a question.
• Explain things clearly, accurately, concisely. (You
don’t want to omit an important part of the full
answer. On the other hand, if you ramble, the chances
might increase that you write something wrong. Give
“the truth, the whole truth, and nothing but the truth”
.)
• Good luck!
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