Section 3: Midterm Review
EWMBA 201A
Eva Vivalt
September 5, 2009
Section 3 Midterm Review
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Administrative Stuff
1.
2.
3.
Prior midterms are on bspace.
Mid-Term Exam is on Tuesday (9/8).
Both cohorts take it then; no lecture on Monday.
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Section 3 Midterm Review
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Review Topics
1.
2.
3.
4.
Decision Trees
Certainty Equivalence
Market Analysis
Questions (especially Thought Questions)
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Section 3 Midterm Review
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Tips for Decision Trees
1.
2.
3.
4.
Start by writing down the CHOICE and CHANCE nodes that you see in
the question.
Try to see relationships among nodes; which come first? Which come later
or are dependent on earlier choices/chances?
Make sure nodes are mutually exclusive (probabilities sum to 1).
After you have a good tree, calculate EVs from right to left.
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Tips for Certainty Equivalence
1.
2.
Translate word problems into two options: one with certain payout and one
with risky payout (and calculate the EV of this risky payout).
Observe decision maker’s choice and apply the following rules to get range
of CE:
1.
2.
3.
If decision maker rejects the option with the certain payout, then her CE is
strictly greater than that payout;
If decision maker accepts the option with the certain payout, then her CE is less
than or equal to that payout.
Compare CE range to EV of the risky payout to determine risk preference:
1.
2.
3.
CE<EV  risk averse
CE=EV  risk neutral
CE>EV  risk loving
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Section 3 Midterm Review
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2005 Decision Tree Question
a.
Draw decision tree and calculate EV (see answer solutions). Note for
future reference that EV = $1.1M.
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2005 Decision Tree Question
b.
If Goodwyn were risk averse, might she have made a different decision
than the one you found in part a? Why or why not?
First think of the intuition: Goodwyn originally took a risky option when
one with a sure payoff existed. A sufficiently risk averse person (i.e.: one
with a CE less than the sure payoff) would not have done this.
We can also see this by considering each of Goodwyn’s choices. To solve,
note that for Goodwyn to be risk averse means we need CE<EV. Now
let’s break the tree into steps and see if there are any situations where the
condition is violated.
i.
ii.
Compare “run as standard story” to “don’t run story”
Compare “run as cover story” to “don’t run story”
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2005 Decision Tree Question
i.
Compare “run as standard story” to “don’t run story”
standard
EV = 0.88
don’t run
0.9
Note if she picked the risky bet with EV = 0.88 (i.e. if she had rejected the safe
bet with payoff 0.9) this would imply that her CE >0.9. But then
CE>0.9>0.88=EV  CE > EV, which we know can’t be true because she is
risk averse (since she is risk averse, she must have CE<EV). So we know she
will pick the safe bet (“don’t run”), and we know she will never choose “run
as standard story”.
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2005 Decision Tree Question
ii.
Compare “run as cover story” to “don’t run story”
cover
don’t run
EV = 1.1
0.9
First, note that if she picked the risky bet with EV = 1.1 (i.e. if she had rejected
the safe bet with payoff 0.9) this would imply that her CE >0.9, but she could
still have a CE<EV. For example, her CE could be 0.99. Second, note that if
she picked the safe bet this would imply that her CE ≤ 0.9, and so her CE <
EV. Hence, in both cases, it could be that her CE<EV, so it is unclear which
one she would pick.
Summarizing, from (i) we know she would never choose “run as standard
story”, but from (ii) we cannot say whether she would choose “run as cover
story” or “don’t run story”.
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Section 3 Midterm Review
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2005 Decision Tree Question
c.
How much would Goodwyn pay for information?
a.
b.
Draw a tree with information node first and calculate EV.
Compare the EV of tree with info to the EV of tree in (a).
cover
Appointed (p= 0.4)
standard
don’t run
2
1
0.9
EV = 2*(0.4) + 0.9*(0.6) = 1.34
cover
Not Appointed (p= 0.6)
standard
don’t run
0.5
0.8
0.9
Note that EV of tree with info = $1.34M, which is $240K greater than the EV of tree in (a).
Hence, Goodwyn would pay up to $240K to obtain the information
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Tips for Market Analysis
1.
2.
3.
4.
To find equilibrium price and quantity set Qd=Qs and use algebra to solve.
For consumer surplus, recall the area of a triangle = ½ * Base * Height
When aggregating a total market demand curve, remember that demand
curves are only additive where they are positive.
Formula for elasticity = (dQ/dp)*(p/Q)
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2006 Market Analysis Question
a.
What is equilibrium price and quantity?
Solve by setting Qd = Qs to find that P* = $150/ton and Q* = 1800K tons.
b.
What is consumer surplus at Q* and P*?
Recall that the area of a triangle is ½ * Base * Height.
Find where demand curve intersects P axis.
This occurs when Q=0, so 0 = 3000 – 8P  P = $375.
Height = ($375 – $150) = $225
Base = 1800K – 0 = 1800K
Hence, consumer surplus = ½ * 1800K * $225 = $202,500,000.
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2006 Market Analysis Question
c.
We have a new demand curve; what is new equilibrium price and quantity?
Step 1: Find where demand is positive:
Plastics: q = 3000 – 8P for P<375
Transportation: q = 2100 – 10P for P<210
Industrial: q = 1760 – 11P for P<160
Step 2: Add demand
0 if P≥375
3000 – 8P if 210≤ P<375
(i.e.: only plastics)
5100 – 18P if 160≤P<210
(i.e.: plastics and transportation)
6860 – 29P if P<160
(i.e.: plastics, transportation and industrial)
Note: the above four lines are the new “Qd”
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2006 Market Analysis Question
c.
We have a new demand curve; what is new equilibrium price and quantity?
Step 3: Find where Qs = Qd; to do this, try different segments of Qd
p,t,i: 6860 – 29P = 12P  P~167, but we require P<160
p,t: 5100 – 18P = 12P  P = 170, this is consistent because 160≤P<210
Plug P* = 170 back into supply (or appropriate demand) to find Q* = 2040K tons.
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2006 Market Analysis Question
What is going on here?
We are trying to figure out where the supply curve intersects the demand curve.
400
Supply here?
350
… or supply here?
300
Price ($)
250
p,t,i
200
p,t
p
150
100
50
demand
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Quantity (K tons)
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2006 Market Analysis Question
d.
Are plastics manufacturers better off?
Compare new consumer surplus with old consumer surplus (calculated in (b)).
When P=170, Qd (plastics) = 3000 – 8*170 = 1640
CS = ½*(1640K - 0)*(375-170) = $168,100K, which is less than before.
Hence, they are worse off.
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Questions?
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