WU Economics Macro Economics Discussion

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ECON 101.082 Introduction to Microeconomics
Q1. (3 points; classes 1-15) Core lessons of the course.
Q2. (3 points; classes 1-4) Willingness-to-pay, marginal analysis, demand curve.
Q3. (5 points; classes 5-8) Competitive equilibrium, Pareto efficiency, first welfare theorem.
Q4. (5 points; classes 9-15) Externalities, utility function, Nash Equilibrium, social optimum.
Q5. (2 points; classes 11-15) Nash equilibrium, taxes, consumer well-being.
Q6. (2 points; classes 11-15) Nash Equilibrium, monopoly, competition.
Bonus. (1 point; classes 17-23) Production possibilities frontier, trade, comparative
advantage, absolute advantage, and returns to scale.
1
Q1. (3 points) Core course lessons.
a)
(2 points) What are the three core lessons of this course? Please list them using
threesentences in total, underline the key word of each sentence.
1.
2.
3.
b)
(0.5 points) What life advice did this course offer? (Is is (1) Economics shows that
peopleshould be selfish because then we get a good outcome for the society as a whole, or
(2) Be good to others, because then we will get an even better outcome for society?)
c)
(0.5 points) What is the intuition behind the result that markets can yield a good
alloca-tion?
2
Q2. (3 points) Willingness to pay, marginal analysis, demand curve.
Jorgenson family’s total willingness to pay schedule for movie tickets is
5 dollars for 1 ticket
12 dollars for 2 tickets
20 dollars for 3 tickets
29 dollars for 4 tickets
40 dollars for 5 tickets
40 dollars for 6 tickets.
The price of a movie ticket is 10 dollars.
a) (2 points) Draw the Jorgenson family’s demand curve for movie tickets.
b) (1 point) How many movie tickets will the Jorgenson family buy?
3
Q3. (5 points) Competitive equilibrium, the first welfare theorem, Pareto efficiency.
a) (1 point) State the first welfare theorem of economics.
b) (2 points) Consider two different scenarios for the world economy for rest of this century.
Scenario 1: Countries invest more on military and less on education, science and
technological innovation. Countries decrease cooperation with one another. The annual
growth rate for the world economy is 0.5% for the rest of the century.
Scenario 2: Countries invest less on military and more on education, science and
technological innovation. Countries further increase cooperation with one another. The
annual growth rate for the world economy is 2.5% for the rest of the century.
How many times bigger will the world economy be at the end of this century in scenario 2
compared to scenario 1?
c) (1 point) Provide the formal proof of the first welfare theorem of economics (i.e.
usealgebra, not graphs to prove it). It is enough to list the relevant inequalities and
describe the logic briefly – there is no need to write extensively.
d) (1 point) An exchange economy has two goods (apples, bananas) and two types of
agents(1, 2). The total endowment of this economy is 7 apples and 7 bananas. Both goods
are divisible goods, so that it is possible to consume fractions of each good (e.g. 4.22
bananas and apples). Each type 1 agent’s preferences are represented by the utility
function
U(x1B,x1A) = 200+x1B+x1A, where x1B and x1A denote the agent’s consumption of bananas and
apples, respectively. Each type 2 agent’s preferences are represented by the utility function
U(x2B,x2A) = ?20 + 3x2B + x2A, where xB2 and x2A denote the agent’s consumption of bananas
and apples, respectively.
4
Use an Edgeworth’s Box to depict the set of Pareto efficient allocations in this economy.
Please capture consumption of bananas on the horizontal axis.
5
Q4. (5 points) Externalities, utility function, Nash equilibrium, social optimum.
Consider an economy with two individuals, agent 1 and agent 2, as well as government. The
two agents value consumption goods and leisure. The preferences of agent 1 are captured by
the utility function
U (C1,L1) = ?100 + 4C1L1,
where C1 denotes consumption of agent 1 and L1 denotes leisure of agent 1. The preferences
of agent 2 are captured by the utility function
U (C2,L2) = ?100 + 4C2L2,
where C2 denotes consumption of agent 2 and L2 denotes leisure of agent 2.
Each agent allocates their time between leisure and education (for simplicity, we do not
model the decision about how much to work after receiving an education). The resource
constraint of agent 1 is
L1 + E1 = 100,
where E1 denotes the level of education of agent 1. Similarly, the resource constraint of agent
2 is
L2 + E2 = 100,
where E2 denotes the level of education of agent 2.
The more education an agent acquires, the more the agent will shift the technological frontier
of the society outward (better iPads and better medicines!). We denote the quality of
technology by A and assume that the quality of technology is given by expression
A = E1 + E2.
Each agent’s consumption is determined by the agent’s own production. Agent’s own
production in turn depends on the agent’s own level of education and on the quality of the
available technology (more educated individuals are better positioned to take advantage of
the newly developed technologies than less educated individuals). Formally, we assume that
6
C1 = E1 + A,
and
C2 = E2 + A.
For analytical simplicity, we assume that each agent can choose either a low level of
education, 40, or a high level of education, 50.
a) (2 points) Construct the payoff matrix.
b) (1 point) Solve for each agent’s best responses.
c) (2 points) Determine each agent’s utility in the Nash equilibrium.
Please write down your final answer here (or as LARGE numbers at the beginning of the
answer in your own sheet): In equilibrium, the utility of agent 1 is
of agent 2 is .
7
and the utility
Q5. (2 points) Nash equilibrium, competition, taxes and subsidies.
Assume that there are many, many firms that sell mobile phones, and assume that the firms’
products are perfect substitutes, so that the supply of mobile phones can be characterized as
perfect competition.
Potential buyers are homogenous in their valuation for mobile phones and each potential
buyer consumes at most 1 mobile phone (“homogenous” means that the consumers are
similar to one another). Suppose that there are 2000 potential buyers and each potential
buyer’s willingness to pay for a mobile phone is 700.
Assume that every firm’s total cost curve is given by TC(q) = 300q, where q is the amount
produced by the firm.
a)
(1 point) Solve for the Nash Equilibrium price. (Please solve for the equilibrium
usinginformal reasoning; please do not draw a payoff matrix).
b)
(1 point) Now assume that the government imposes a 200 dollar tax on every
mobilephone sale. (Every time a phone is sold, the firm selling the phone must pay
government 200 dollars). What is the impact of this tax on consumer well-being?
8
Q6. (2 points) Nash equilibrium, monopoly, competition.
Assume that there are N firms that can produce and sell mobile phones, where N is a positive
integer, and assume that when N > 1 the firms’ products are exactly alike (when N = 1 there
is just one seller). N is thus a fixed number, and everyone knows which that number is (N is
common knowledge).
Potential buyers are homogenous in their valuation for mobile phones and each potential
buyer consumes at most 1 mobile phone. Suppose that there are 1000 potential buyers and
each has a willingness to pay $600 for a mobile phone
Assume that each firm’s total production costs TC(q) are given by the function TC(q) =
300000 + 200q when q > 0 and TC(q) = 0 when q = 0. Here q denotes the quantity produced
by the firm. Assume that firms choose prices and that the firms choose their prices
simultaneously and non-cooperatively.
a) (1 point) Determine the equilibrium price when N = 1.
b) (1 point) Determine the equilibrium price when N > 1.
Bonus. (1 point) Production possibilities frontier, gains from trade, comparative advantage,
absolute advantage, and returns to scale.
Suppose that there are two countries, A and B. The production possibilities frontier of
?
?
country A is given by
coconutsA +
fishA = 8, and the production possibilities frontier
?
?
of country B is given by coconutsB + fishB = 8 where coconutsi denotes the amount of coconuts
produced by country i and fishi denotes the amount of fish produced by country i.
9
Assume that the utility function of each country i is given by the expression
U(coconutsi,fishi) = min(coconutsi,fishi)
where coconutsi denotes the amount of coconuts consumed by country i and fishi is the
amount if fish consumed by country i.
Suppose that all gains from trade are divided equally between the countries.
Determine the utility of each country when the agents can trade.
Write the utility of country A here
and the utility of country B here
and provide a detailed explanation below (if you submit answers on your own answer sheet,
please write these numbers using LARGE print).
10
Econ 101: Introduction to Microeconomics, Winter 2022, University of Waterloo.
During WEEKS 1-8 of the course we have covered the three key lessons of this course.
These key lessons are:
Lesson 1. Economists assume that when people make choices, they carefully evaluate the
costs and bene…ts and make good choices. We have referred to this assumption as “behavior
is optimization”.
Lesson 2. When our choices do not have direct external e¤ects on other people, self-interest
and voluntary trade (markets) alone lead to good allocations. We have have formally expressed this result as the “First Welfare Theorem”, according to which any
competitive equilibrium is Pareto Efficient (assuming there is a lot of competition and
there are no externalities).
Lesson 3. When our choices do have direct external e¤ects on other people, government
intervention can result in a better allocation than the allocation determined by self-interest
and markets alone. Externalities thus form an economic rationale for government
intervention”.
Lesson (1) is important for two reasons. First, the assumption that “behavior is rational”
is what sets economics apart from other social sciences such as sociology and psychology.
Second, this assumption is the starting point for most modern economic analyses. That
said, recently a growing number of economists have started to question the validity of this
assumption. The …eld within economics that studies such departures from rationality is
called as “behavioral economics”. We will talk about those departures from ratonality in
week 12.
Lessons (2) and (3) in turn are important because result (2) is economists’key theoretical
justi…cation for advocating market-oriented economic policies and solutions and because
60
result (3) tells both economists and governments that markets have their limits in terms of
allocating goods e¢ ciently.
My hope is that by focusing on lessons (1), (2), and (3) during weeks 1-8, you will remember
these lessons forever and that you will remember that these three lessons are the three core
lessons of economics.
During weeks 1-8 we have also learned a number of important tools that economists use,
including:
Tool 1. Willingness to pay.
Tool 2. Marginal analysis
Tool 3. Budget constraint with income.
Tool 4. Budget constraint with endowment.
Tool 5. Indi¤erence curves.
Tool 6. Utility function.
Tool 7. The model of exchange.
Tool 8. Competitive equilibrium.
Tool 9. Pareto e¢ ciency.
Tool 10. Payo¤ matrix
Tool 11. Best response.
Tool 12. Nash equilibrium
Tool 13. Game tree
Tool 14. Subgame-perfect Nash equilibrium
Tool 15. Backward induction
61
Please write your University ID Number here:
DO NOT WRITE YOUR NAME ANYWHERE ON THE EXAM
Most questions in this exam are very challenging. This is by design; it will
make the final exam feel much easier.
University of Waterloo
Winter 2022
ECON 101.082 Introduction to Microeconomics
Midterm Exam 2 (Due Mar 11, 1159pm.)
You can submit answers either (1) written into this PDF or (2) written on
empty sheets (electronic or paper–scan) and submitted as a PDF.
Please submit all answers in one PDF file to the Dropbox on Learn.
In either case, please write student ID number at the top. No names anywhere,
please.
The maximum points total is 20 points+1 bonus point. The highest possible grade is 105%.
You have unlimited minutes to complete the exam. Budget your time well and show your
work. Good luck!
1
Q1. (3 points) Take-home message of the course. This question is repeated in every exam.
a) What are the three core lessons of this course? Please list them using three sentences in
total, underline the key word of each sentence.
1. (1 point) What is the key behavioral assumption that economists almost always make in
their analyses?
2. (1 point) What is the main advantage of market economies relative to command economies?
(hint: relates to efficiency, not equality).
3. (0 points; we haven’t covered it yet)
b) (0 points; we haven’t covered it yet) What life advice does this course offer?
c) (1 point) What is the intuition behind the result that markets can yield a good allocation?
2
Q2. (5 points) Willingness to pay, marginal analysis, and the demand curve
a) (4 points) George and Maria are the only consumers in an economy. George’s total
willingness to pay schedule for sunglasses is
150
160
170
180
180
dollars
dollars
dollars
dollars
dollars
for
for
for
for
for
1
2
3
4
5
pair
pairs
pairs
pairs
pairs
Maria’s total willingness to pay schedule for sunglasses is
100
100
100
100
100
dollars
dollars
dollars
dollars
dollars
for
for
for
for
for
1
2
3
4
5
pair
pairs
pairs
pairs
pairs
The price of a pair of sunglasses is $20.
Draw the Market demand curve for sunglasses. Market demand curve shows for any
given price how many units in total consumers in this economy would buy. Please
draw price on the vertical axis and quantity on the horizontal axis.
3
b) (1 point) There are 900 potential buyers for a mobile phone in a market. The potential buyers are heterogenous in their valuation for mobile phones and each potential buyer
consumes at most 1 mobile phone. In other words, no potential consumer sees any value
for a second mobile phone. The word “heterogenous” means that the potential buyers are
different from one another.
The potential buyers differ in their willingness to pay for a phone. These willingness to pays
are uniformly distributed between 1 and 900. Hence, someone has willingness to pay 900,
someone has willingness to pay 899, someone has willingness to pay 898,…, someone has
willingness to pay 2, and someone has willingness to pay 1 for a mobile phone.
Please draw the market demand curve for mobile phones. (Again: Market demand curve
shows for any given price how many units in total consumers in this economy
would buy. Please draw price on the vertical axis and quantity on the horizontal
axis.)
4
Q3. (4 points) Pareto Efficiency and the Utility Function.
a) (2 points) Seven’s preferences satisfy the following strict preference relations:
(2 oranges, 2 apples) ? (2 oranges, 1 apple)
(2 oranges, 1 apple) ? (1 orange, 2 apples)
(1 orange, 2 apples) ? (2 oranges, 0 apples)
(2 oranges, 0 apples) ? (0 oranges, 2 apples)
(0 oranges, 2 apples) ? (1 orange, 1 apple)
(1 orange, 1 apple) ? (1 orange, 0 apples)
(1 orange, 0 apples) ? (0 oranges, 1 apple)
(0 oranges, 1 apple) ? (0 oranges, 0 apples)
Seven’s preferences are also transitive, complete and reflexive.
Marcellus’ preferences are the same as Seven’s preferences.
Suppose that Seven and Marcellus are the only agents of an exchange economy, and that the
endowment of Seven is (1 orange, 1 apple) and the endowment of Marcellus is (1 orange, 1
apple).
For this economy, please list all the allocations which are NOT Pareto efficient. (If all
potential allocations are Pareto efficient, please answer ”All potential allocations are P.E.”).
5
b) (2 points) An exchange economy has two goods (apples, bananas) and two types of
agents (1, 2). Endowment of agent 1 is (3 bananas, 3 apples), and endowment of agent 2
is (5 bananas, 2 apples). Both goods are divisible goods, so that it is possible to consume
fractions of each good (e.g. 2.44 bananas and 45 apples). Each type 1 agent’s preferences are
represented by the utility function U (x1B , x1A ) = min{x1B , x1A }, where x1B and x1A denote the
agent’s consumption of bananas and apples, respectively. Each type 2 agent’s preferences
are represented by the utility function U (x2B , x2A ) = 5 min{x2B , x2A } where x2B and x2A denote
the agent’s consumption of bananas and apples, respectively.
Use an Edgeworth’s Box to depict the set of Pareto efficient allocations in this economy.
Please capture consumption of bananas on the horizontal axis.
6
Q4. (8 points) Competitive equilibrium and the first welfare theorem.
a) (1 point) State the first welfare theorem of economics.
b) (1 point) Provide the definition of a Pareto Efficient allocation.
c) (1 point) Suppose that a crazy mad dictator allocates all resources in an economy. The
dictator gives some resources to every individual. Would the resulting allocation likely be a
Pareto Efficient allocation? Answer either ”YES” or ”NO” in big letters and then explain
in 1 sentence.
d) (1 point) Suppose that a benevolent dictator allocates all resources in an economy. The
dictator gives some resources to every individual. Would the resulting allocation likely be a
Pareto Efficient allocation? Answer either ”YES” or ”NO” in big letters and then explain
in 1 sentence.
7
e) (2 point) Suppose that initially a market economy and a command economy are equally
developed (in that their economies are just as large) and suppose that the market economy
grows at rate 2.0% per year and the command economy grows only a little bit slower, at rate
1.0% per year. Approximately how long will it take for the market economy to be twice as
wealthy as the command economy?
Hint: We have not covered the formulas for calculating this. It may be useful to review the
relevant high-school math (or google the relevant formulas) to do this important calculation.
f) (2 points) Provide the graphical OR formal proof of the first welfare theorem of economics.
8
Bonus. (1 point) Assume that there are N firms that sell mobile phones, where N is a
positive integer. Assume also that when N > 1 the firms’ products are exactly alike (when
N = 1 there is just one seller). N is thus a fixed number, and everyone knows which that
number is (N is common knowledge).
Potential buyers are homogenous in their valuation for mobile phones and each potential
buyer consumes at most 1 mobile phone. Suppose that there are 900 potential buyers and
each has a willingness to pay $500 for a mobile phone. (The term “homogenous” means that
the potential buyers are identical, exactly alike one another.)
Assume that each firm’s total production costs T C(q) are given by the function T C(q) =
250q, where q is the quantity of mobile phones produced by the firm. Assume that firms set
their prices for mobile phones simultaneously and non-cooperatively.
What is your prediction (as an economist) for the market price of mobile phones as a function
of the number of firms N ? Please state the answer and explain as briefly as possible.
9
Please write your University ID Number here:
DO NOT WRITE YOUR NAME ANYWHERE ON THE EXAM
University of Waterloo
Winter 2022
ECON 101.082 Introduction to Microeconomics
Midterm Exam 1 (Due Feb 7, 1159pm.)
You can submit answers either (1) written into this PDF or (2) written on
empty sheets (electronic or paper–scan) and submitted as a PDF.
Please submit all answers in one PDF file to the Dropbox on Learn.
In either case, please write student ID number at the top. No names anywhere,
please.
The maximum points total is 20 points+1 bonus point. The highest possible grade is 105%.
You have unlimited minutes to complete the exam. Budget your time well and show your
work. Good luck!
1
Q1. 1 point) Take-home message of the course. This question is repeated in every exam.
a) What are the three core lessons of this course? Please list them using three sentences in
total, underline the key word of each sentence.
1. (1 point)
2. (0 points; we haven’t covered it yet)
3. (0 points; we haven’t covered it yet)
b) (0 points; we haven’t covered it yet) What life advice does this course offer?
c) (0 points; we haven’t covered it yet) What is the intuition behind the result that markets
can yield a good allocation?
2
Q2. (6 points) George’s total willingness to pay schedule for sunglasses is
160
160
160
160
160
dollars
dollars
dollars
dollars
dollars
for
for
for
for
for
1
2
3
4
5
pair
pairs
pairs
pairs
pairs
The price of a pair of sunglasses is $20.
a) (3 points) How much money will George spend on sunglasses? (Please remember to show
your work!)
b) (2 points) Draw George’s demand curve for pairs of sunglasses.
c) (1 point) If George first gets two pairs of sunglasses for free (as a gift), how much money
will he then spend on purchasing additional pairs of sunglasses? Continue to assume that
the price of each pair of sunglasses is $20.
3
Q3. (4 points) Jerry lives in an economy with two goods: bananas and apples. Bananas
cost $3 each and apples cost $4 each. Suppose that Jerry is an optimizing consumer with
indifference curves that are strictly convex, and that we observe that Jerry buys 3 bananas
and 3 apples. Draw a graph that shows Jerry’s (1) budget constraint, (2) optimal consumption point, (3) the indifference curve that goes through the optimum point, and (4) the
indifference curve that goes through point (2 bananas, 2 apples).
In your graph, please place quantity of apples on the horizontal axis.
4
Q4. (3 points) Jen only consumes Kraft dinners and steaks. One day, Jen’s income increases,
with no change in the price of steaks and no change in the price of Kraft dinners. Assume
that Jen’s preferences are strictly convex, transitive, and that she always prefers more to
less.
a) (1 point) Using a graph of indifference curves and budget constraints, show that the income
increase can lead to a decrease in Jen’s consumption of Kraft dinners. Draw a graph that
shows each budget constraint, both optimal consumption point (before and after income
change), and any indifference curve that goes through either optimum point. Carefully label
each axis, each budget constraint, and each optimum. Place quantity of Kraft dinners
on the horizontal axis.
b) (1 point) Repeat (a) but now show that the income increase can lead to an increase
in Jen’s consumption of Kraft dinners (obviously, she then has different tastes than those
depicted in (a)).
b) (1 point) Can the income increase lead to a decrease in Jen’s well-being? Write either
”YES” or ”NO” in big letters.
5
Q5. (2 points) Frankie consumes only juice (OJ) and chocolate milk (CB). As always
in this course, we assume that Frankie is an optimizing individual with preferences that
are transitive, complete, reflexive and strictly convex. An economist observes prices and
Frankie’s consumption choices for 2 months. The economist collects the following data on
Frankie’s consumption (q denotes quantity, p denotes price):
month qOJ qCB pOJ pCB
may
2
4
4
4
jun
1
5
4
2
a) (1 point) In one graph, plot Frankie’s budget constraint and optimal choice for
each month. In this same graph, plot also each indifference curve that goes any
optimum. Please draw consumption of juice on the horizontal axis.
b) (1 point) Can it be determined whether Frankie is better off in May or June? Write one
off the following: ”IT CANNOT BE DETERMINED” or ”Frankie is better off in May” or
”Frankie is better off in June”.
6
Q6. (2 points) Ned lives in a large town that has no money. Ned’s preferences do not
change from one day to another. He produces and consumes only oranges and apples. Ned’s
daily production is 5 oranges and 3 apples. On Monday, after trading in the Town Market,
Ned consumes 4 oranges and 4 apples. Suppose that Ned’s endowment on Tuesday is again
(5 oranges, 3 apples) . The prices on the Market are different on Tuesday. More specifically,
suppose that the relative price of oranges is higher on Tuesday than on Monday.
In one graph, please draw and label (1) budget constraint on Monday, (2) budget constraint
on Tuesday, (3) optimal consumption point on Monday, (4) optimal consumption point on
Tuesday, (5) indifference curve that goes through Monday’s optimum, (6) indifference curve
that goes through Tuesday’s optimum, and (7) indifference curve that goes through the
endowment point. Draw consumption of oranges on the horizontal axis.
7
Q7. (2 points) Levi’s total willingness to pay schedule for chocolate bars is
16
27
36
37
37
dollars
dollars
dollars
dollars
dollars
for
for
for
for
for
1
2
3
4
5
bar
bars
bars
bars
bars
Levi can only buy chocolate bars at ChocoMax. Assume also that Levi is ChocoMax’s only
potential customer. Assume that ChocoMax chooses pricing so that it maximizes it’s profit
(revenue-costs). ChocoMax’s cost of producing each chocolate bar is 4 dollars. Currently
ChocoMax can sell chocolate bars either individually or in pairs of two.
Would Levi’s well-being increase if bundling (i.e. selling choco bars in pairs of two) were
made illegal?
8
Bonus Q. (1 point) It is 200 AD. and a slave is thrown into a gladiator arena. N hungry
lions are lined up behind the gate to the gladiator arena. In the line of lions each lion is
bigger and stronger than the lion in front of it. N is a known strictly positive integer. All
lions know N and all lions know that all other lions know N, etc (i.e. in economics jargon
the number of lions N is common knowledge).
In the beginning of the event, a slave is standing in the middle of the arena. The gate is
then opened to let the weakest lion enter the arena (the weakest lion is of course the first
lion in the line of N lions). Any lion that is let into the arena always chooses between eating
and not eating the prey in the arena. If a lion eats its prey, the next weakest lion in the
remaining line of lions is let into the arena. If a lion refuses to eat its prey, all lions are
immediately escorted out of the arena and and no further lions are let into the arena. Thus
the first lion’s prey is the slave. For all other lions the lion’s potential prey is the lion that is
in front of it in the line of lions outside the gates of the arena in the beginning of the game.
A lion prefers being hungry to being dead, and a lion prefers being full and alive to being
hungry and alive.
Will the slave be eaten?
9
Q1a) “Behavior is optimization” or “people are rational” or “people carefully evaluate the costs
and benefits of each option and then make an optimal decision” or something similar.
Q2a)
MWP for 1st pair: $160
MWP for 2nd pair $160-$160=$0
MWP for 3rd pair $160-$160=$0
MWP for 4th pair $160-$160=$0
MWP for 1st pair $160 is greater than cost $20. Hence buys first pair of glasses.
MWP for 2nd pair $20 is lower than cost $20. Hence does not buy more glasses.
Conclusion: Spends $20 to buy 1 pair of glasses.
Q2b)
Q2c) MWP for 3rd pair $0 is less than cost $20. Hence would spend $0 dollars on additional
pairs of glasses.
Q3)
Q4ab)
4c) “NO”. An increase in our salary can never makes us unhappy!
5a)
5b) Frankie is better off in May than June. This is revealed by the fact that in May the
combination that Frankie chose in June was affordable but Frankie did not choose it: the
explanation is that Frankie views the combination chosen in May to be better than the
combination chosen in June.
Q6)
Q7) First solve for Levi’s net benefit when there is no bundling.
To do this we first need to solve for Levi’s MWP schedule.
MWP for 1st: 16
MWP for 2nd: 27-16=11
MWP for 3rd: 36-27=9
MWP for 4th: 37-36=1
MWP for 5th: 37-37=0
Let p denote price. Now we know that
If p=16 -> Levi will buy 1
If p=11 -> Levi will buy 2
If p=9 -> Levi will buy 3
If p=1 -> Levi will buy 4
Now solve for the firm’s optimal price:
p=16 -> Profit=revenue-cost=16×1-4×1=12 (because will then sell 1)
p=11 -> Profit=revenue-cost=11×2-4×2=14 (because will then sell 2)
p=9 -> Profit=revenue-cost=9×3-4×3=15 (because will then sell 3)
p=1-> Profit=revenue-cost=1×4-4×4=-12 (because will then sell 4)
The profit maximizing price is thus p=9.
When the firm sets price at p=9, Levi will buy 3 units and his net benefit will be
TWP-costs=36-9×3=9
Next solve for Levi’s net benefit when there is bundling.
To do this we first need to solve for Levi’s MWP schedule for pairs.
MWP for 1st pair: 27
MWP for 2nd pair: 37-27=10
MWP for 3rd pair: 27-37=0
Let p denote price. Now we know that
If p=27 -> Levi will buy 1 pair
If p=10 -> Levi will buy 2 pairs
Now solve for the firm’s optimal price for a pair:
p=27 -> Profit=revenue-cost=27×1-4×2=19 (because will then sell 1 pair)
p=10 -> Profit=revenue-cost=10×2-4×4=4 (because will then sell 2 pairs)
The profit maximizing price for a pair is thus p=27
When the firm sets price of a pair at p=27, Levi will buy 1 pair and his net benefit will be
TWP-costs=27-27=0
Finally we compare Levi’s net benefit with versus without bundling.
Without bundling, Levi’s net benefit (in terms of money): $9.
With bundling, Levi’s net benefit (in terms of money): $0.
Hence Levi would be better off if bundling were made illegal.
Bonus. This question is solved backwards (the technical term is “Backward induction”).
What would the last lion do? The last lion would always eat the pray because he has nothing to
fer.
What would the second last lion do? The second last lion KNOWS that the last lion would
always eat the pray and thus the second last lion would never eat the pray.
What would the third last lion do? The third last lion KNOWS that the second last lion would
never eat the pray and thus the third last lion would always eat the pray.
What would the fourth last lion do? The fourth last lion KNOWS that the third last lion would
always eat the pray and thus the fourth last lion would never eat the pray.
This reveals a pattern: If the number of lions is odd, then the slave would get eaten. If the
number of lions is even, then the slave would survive.

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Macro Economics

values of quantity

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