intermediate microeconomics assignment

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Final Exam - Spring 2020 Solutions

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Preview text, final exam [200 points], econ 201-3: intermediate microeconomics.

Distributed May 5, 2020 at 10:30 AM EDT Due May 6, 2020 at 10:30 AM EDT

Please show all of your work in answering the following questions. Points will be awarded for the development and presentation of your answers, as well as your final answers.

Your answers must betypedin Microsoft Word, LaTeX, or similarly suitable word processor. A Word template and LaTeX template will be provided to you. Please type your answers to each question directly underneath each part (e., for part 1(c), please type your answer between question 1(c) and question 1(d)). Do not remove the page breaks. Submissions that are not typed will incur a 10 point penalty.

You are not permitted to discuss this exam with any other person may use your notes, textbooks, online resources, etc. By submitting this exam for grading, you affirm that you have not communicated with any person about this exam and have adhered to the honorcode. Exams must be submitted on Canvas by the deadline to be accepted. Good luck and have a great summer!!!

Problem 1 [30 Points]

Kramer and Mickey play a version of Rock-Paper-Scissors, although not the version we considered in Homework 8. Please watch this video.

(a) What is the Nash equilibrium of the game that Kramer and Mickey are playing? [5 points]

Both Kramer and Mickey have a dominant strategy to play “rock.” This of course is not the case in the actual rock-paper-scissors game, where there are no pure strategy Nash equilibria.

(b) The payoff matrix for the game is given below. Find all values ofxfor which both players will follow the Nash equilibrium that you found in (a). [10 points]

Mickey R P S

R x,x -2,3 3,- P 2,-3 0,0 -4, S -3,2 4,-5 0,

For both plays to play “rock,” the value ofxmust be at least 3. Whenx≥3, neither player has an incentive to deviate from the Nash equilibrium where both players play rock.

R 0,0 -2,2 1,-

P 2,-2 0,0 -2,, s -1,1 2,-2 0,.

Find all pure-strategy and mixed strategy Nash equilibria. If there arenone, then state “there are none.” [15 points] There are no pure-strategy Nash equlibrium. The mixed strategy Nash equilibrium is ( 25 , 15 , 25 ) for both players (i., play R with probability 2/5, P with probability 1/5 and S with probability 2/5).

Problem 2 [40 Points]

Two firms – Top of the Muffin to You! (TMY) and Muffin Tops (MT) – are considering entering the newly established muffin top market. TMY and MT are the only possible entrants/potential participants in the muffin top market. The firms will sell just the muffin top to their customers. Entry costs are considerable because the firms have to develop a method to dispose of the muffin stumps.

Subgame (5) is a simultaneous move game. The NE of this subgame is for both players to price high.
TMY can enter aggressively for a payoff of 10, enter passively for a payoff of 5, ornot enter for a payoff of 5. Hence, TMY will enter aggressively.

Therefore, the subgame perfect Nash equilibrium is

Subgame 1: TMY enters aggressively
Subgame 2: TMY prices low
Subgame 3: MT prices high
Subgame 4: MT prices low
Subgame 5: Both TMY and MT price high

Problem 3 [50 Points]

U. states are quickly trying to acquire personal protective equipment, including latex gloves. Two firms – Vandelay Industries and Kruger Industrial Smoothing – willsell gloves to the states. For Vandelay Industries, the per glove costs are 2 for materials, 5 for production and 3 for shipping. For Kruger Industrial Smoothing, the per glove costs are 3 for materials, 6 for production, and 1 for shipping. Letp 1 be the price per pair of gloves that Vandelay Industries charges andp 2 be the price per pair of gloves that Kruger Industrial Smoothing charges. Both firms set prices simultaneously and maximize profit. The states will buy gloves from the firm with the lower price. If both firms charge the same price, the states will buy an equal number of pairs from each firm. The states demand for pairs of gloves isQ(p) = 100− 2 pfor any pricep.

(a) What are the Nash equilibrium prices? How much does each firm earn? Justify your answer. [ points] Both firms have marginal cost of 10 and will set price equal to marginal cost bythe same argument we used in class. Both groups earn zero profit.

(b) What prices would the firms charge if they agreed to maximize theirjoint profit? How much does each firm earn? [5 points] The joint profit function is

π= (p−10)(100− 2 p)

Taking the first-order condition and solving for price, we findp= 30 andπ= 800. Hence, each firm earns 400.

(c) Suppose Vandelay Industries abandons the agreement in (b) and decides to maximize its own profit. Kruger Industrial Smoothing will set the same price you found in (b). Assuming Vandelay must set an integer price (i., no cents), what price should Vandelay Industries set? How much profit does each firm earn? [10 points] Vandelay should set price equal to 29 and will make 798 in profit, while Kruger will make 0.

(d) Epidemiologists now say that coronavirus will go on forever. The two firms decide to make the following agreement:

(i) Each firm will initially agree to cooperate and set the price that maximizes their joint profit. (ii) Each firm will continue to set the cooperation price for all subsequent periods, provided that the other firm does as well. (iii) Deviations from the cooperation price will be punished by setting the single-period Nash equilibrium price in every period thereafter.

You can assume the normal-form representation of the single period game isgiven by

Kruger Cooperate Defect

Vandelay Cooperate 50,50 0, Defect 100,0 0,

Note that these are not the profits you found in parts (a)-(c). Future payoffs are discounted by a factorδper period. For what values ofδis the strategy described in the problem a subgame perfect Nash equilibrium? [15 points] If a firm decides to follow the grim trigger strategy, it will receivea profit of 50 in each period. Hence, the payoff from cooperating is

50 +δ(50) +δ 2 (50) +.. .=

1 −δ If a group deviates from the grim trigger strategy, it will receive 100 in the first period and 0 in every period thereafter. Hence, the payoff from deviating is 100. So there will be a subgame perfect Nash equilibrium if

1 −δ ≥ 100 ⇔ δ≥

(e) Supposeδ= 56. The states will offer each firm a bonusbif they both defect. What is the value ofbthat makes the firms indifferent between adopting and not adopting the strategy described in (d)? [15 points] If a firm decides to follow the grim trigger strategy, it will receivea profit of 50 in each period. Hence, the payoff from cooperating is

50 + (50) +δ 2 (50) +.. .=

If a firm deviates from the grim trigger strategy, it will receive 100 in the first period andbin every period thereafter. Hence, the payoff from deviating is

100 +δb+δ 2 b+.. .= 100 + bδ 1 −δ

Setting 300 = 100 + 5b, we findb= 40

(b) Find the optimal wagewand finef if Vandelay Industries can monitor George’s effort level. [ points] We know from above that if we want George to slack off, we should setw= 400 and f = 0. Expected profit is 2000. If we want George to work hard, then we only need a participation constraint:

w−f−20) = 20

Because George is risk averse, we knoww=w−f, which impliesf= 0. Solving the above equation forw, we findw= 1600. Expected profit for Vandelay Industries is

π=((5−1)1000−1600) +.3((5−1)500−1600) = 1800< 2000

Hence, we should setw= 400 andf= 0. Expected profit is 2000.

(c) What is the most Vandelay Industries would be willing to pay fora desk camera that monitors George’s effort level? [13 points] Zero! Vandelay Industries should simply pay a wage of 400 and not assess a penalty because he earns a higher expected payoff if George slacks off.

(d) Assume Vandelay Industries cannot observe George’s effort level would the high output level have to be for Vandelay Industries to be indifferent between George working hard and slacking off? Everything besides the high output level remains the same in thisproblem. [12 points] Letxdenote the high output level. If George exerts high effort, Vandelay’sexpected profit is

πH=(4x−2704) +.3(2000−144) = 2. 8 x− 1336

if George exerts low effort, Vandelay’s expected profit is

πL=(4x−400) +.8(2000−400) = 0. 8 x+ 1200

EquatingπH=πLand solving forx, we findx= 1268.

Problem 5 [50 Points]

Mr. Gesundheit is worried he might contract coronavirus and is considering buying health insurance from Feeling Blue. Feeling Blue believes there is a 40% chance thatGesundheit will get coronavirus and be costly to insure. He will offer Gesundheit two insurance plans: (1) a comprehensive plan with price/premiumpHand actuarial valueqHand (2) a skimpy plan with price/premiumpLand actuarial valueqL. Mr. Gesundheit has utility functionui= (100θi)q−p, whereqis the actuarial value of the plan (e., if the actuarial value is 10%,q= 10),pis its price/premium, andiis Mr. Reckless’ type such thatθL= andθH=. If Gesundheit does not buy insurance, he can file for bankruptcy as “implicit insurance.” It is costless to Gesundheit to file for bankruptcy. Bankruptcy will cover 10% of Mr. Gesundheit’s expected costs. The expected cost of an insurance plan with valueqisc(q) =. 5 q 2.

(a) What are the constraints we need in this problem? Which of these constraints are binding? [ points]

P CH: 80qH−pH ≥ 80(10) P CL: 50qL−pL ≥ 50(10) ICH: 80qH−pH ≥ 80 qL−pL ICL: 50qL−pL ≥ 50 qH−pH

The first (P CH) and fourth (ICL) are not binding

(b) Find the optimal bundles (qL, pL) and (qH, pH) that maximize Feeling Blue’s expected profit. [ points] FromP CL, we obtainpL= 50qL−500. FromICH, we obtainpH = 80qH− 30 qL−500. The expected payoff function now becomes

π= 0(80qH− 30 qL− 500 −. 5 qH 2 ) + 0(50qL− 500 − 0. 5 qL 2 )

Taking the first order conditions with respect toqH, we findqH = 80. Taking the first order condition with respect toqL, we findqL= 30. Hence,pL= 50(30)−500 = 1000, pH= 80(80)− 30(30)−500 = 5000, andπ= 1050.

(c) How much would you be willing to pay Dr. Fauci to find out if Mr. Gesundheit will get coronavirus and be costly to insure? [10 points] If Gesundheit is a high type, we can offer him the high contract. We onlyneed theP CH. So the problem is

π=pH−. 5 qH 2 = 80qH− 800 −. 5 qH 2

Taking the first-order condition and solving, we findqH= 80,pH= 5600, andπH= 2400. If Gesundheit is a low type, we can offer him the low contract. We onlyneed theP CL. So the problem is

π=pL−. 5 qL 2 = 50qL− 500 −. 5 qL 2

Taking the first-order condition and solving, we findqL= 50,pL= 2000, andπL= 750. So Feeling Blue’s expected profit after paying an epidemiologist is(2400) +.6(750) = 1410. So the firm would be willing to pay 1410−1050 = 360 to find out if Gesundheit is a high or low type.

(d) Suppose Dr. Fauci actually charges 480. What is the probability of Gesundheit contracting coro- navirus that would make Feeling Blue indifferent between hiringand not hiring Dr. Fauci? [ points] Feeling Blue’s expected profit when the type is unobserved is

π=α(80qH− 30 qL− 500 −. 5 qH 2 ) + (1−α)(50qL− 500 − 0. 5 qL 2 ) = 1800α+ 550(1−α)

Multiple Choice

Course : Intermediate Microeconomics (ECON 201)

University : emory university.

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Prof. Jonathan Gruber

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Principles of microeconomics, midterm exam 1.

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Preparation

Midterm exam 1 covers material from the beginning of the course:

Unit 1: Supply and Demand
Unit 2: Consumer Theory

The exam tests your conceptual, mathematical and graphical understanding of the material covered in this portion of the course.

Content Review

Please review the content from the units covered before attempting the exam. The summary notes below are concise outlines of the main points covered in each session, but are presented only as a study aid in reviewing for the exam. They do not provide the in-depth knowledge needed to successfully complete the exam problems.

Midterm 1 Summary Notes (PDF)

Practice Exams

Once you are comfortable with the course content, complete the following practice exams. These exams are from Professor William Wheaton’s course, 14.01 Principles of Microeconomics from Fall 2007, and are used with permission.

Practice Midterm 1 Problems (PDF)
Practice Midterm 1 Solutions (PDF)

Exam Problems and Solutions

The exam should be completed in 2 hours. This is a closed book exam. You are not allowed to use notes, equation sheets, books or any other aids.

Midterm 1 Problems (PDF)
Midterm 1 Solutions (PDF)

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Felix Munoz-Garcia

Professor – School of Economic Sciences, Washington State University

EconS 301, Intermediate Microeconomic Theory with Calculus

Syllabus – EconS 301
Chapter 1 – Introduction
Chapter 2 – Consumer Preferences and Utility
Revealed Preferences, Handout
Chapter 4 – Substitution and Income Effects
Chapter 5 – Measuring Welfare Changes
Chapter 6 – Choice under Uncertainty
Chapter 7 – Production Functions
Chapter 8 – Costs and Cost Minimization
Chapter 9 – Partial and General Equilibrium (Perfectly competitive markets)
Chapter 10 – Monopoly and Monopsony
Chapter 11 – Price Discrimination and Bundling
Chapter 12 – Simultaneous-move Games
Chapter 13 – Sequential and Repeated Games
Chapter 14 – Imperfect Competition
Chapter 15 – Games of Incomplete Information and Auctions
Chapter 16 – Contract Theory
You can find more materials in Intermediate Microeconomic Theory: Tools and Step-by-Step Examples , MIT Press, Link .
Math Review
Review Session 1
Review Session 2
Review Session 3
Review Session 4
Review Session 5
Review Session 6
Review Session 7
Review Session 8
Review Session 9
Review Session 10
Review Session 11
Review Session 12
Review Session 13
For exercises with detailed answer keys, see Practice Exercises for Intermediate Microeconomic Theory , with detailed answers to over 310 exercises, Link .
How to compute your overall grade in the class: Link.