## Microeconomics

Microeconomics

Order Description

Your submission should be typed and formatted appropriately (including equations!). Graphs, when required, can be drawn by hand, scanned and inserted in the submitted

document, or can be drawn using a software of your choice. In both cases, please insert them in the text of the corresponding exercise (do not include them at the end

of your document). Penalty will apply if you fail to follow these recommendations.

You should attempt to solve all the assigned problems and provide concise but detailed, and clearly explained, answers to the questions. This coursework should be

submitted individually. Students will be marked for their individual contribution and the papers submitted will be checked for plagiarism.

SESS2005

Topics in Microeconomics

Coursework

February 2015

Due: Thursday 26th of February at 4.00 pm

Submission: Submit a hard-copy to the school office and on Moodle for plagiarism checks.

Your submission should be typed and formatted appropriately (including equations!). Graphs, when required, can be drawn by hand, scanned and inserted in the submitted

document, or can be drawn using a software of your choice. In both cases, please insert them in the text of the corresponding exercise (do not include them at the end

of your document). Penalty will apply if you fail to follow these recommendations.

You should attempt to solve all the assigned problems and provide concise but detailed, and clearly explained, answers to the questions. This coursework should be

submitted individually. Students will be marked for their individual contribution and the papers submitted will be checked for plagiarism.

Part A [30 points]

Two leading video game companies, Game4U and All4Gamers, have each a new game ready for release. They also both know that their direct concurrent is about to release a

new game as well. December would be the best time to release their games as young players will be on holidays and may have pocket money to spend on games, or may ask

to receive the game for Christmas. However, having both games out at the same time will mean that the companies are in direct competition and are likely to make a

lower profit than if the games were to be released at different times. Two other release dates are possible: either October, so that the game can build interest and

sales may hold on till Christmas; or March, hoping to benefit from a rise in sales around Easter.

1. Assuming that both firms have to announce the release date for their games simultaneously (static game with perfect but incomplete information), the payoff matrix

showing the likely profit associated with all possible strategies, is as follows:

Payoffs (Game4U, All4Games)

In £10,000

All4Gamers

December

October

March

Game4U

December

25,25

150,100

150,50

October

100,150

0,0

100,50

March

50,150

50,100

-25,-25

a. Is there a dominant strategy for Game4U? And for All4Gamers?

b. Is there a pure strategy Nash Equilibrium for this game? Explain.

2. Let’s assume now that the two firms act sequentially. First Game4U announces a release date for its new game, and then All4Gamers announces a release date for its

new game.

a. Draw the associated pay-off diagram, assuming the payoffs for each set of strategies remain as above.

b. Is there a pure strategy Nash equilibrium for this game? Explain your answer. Does it differ from the conclusion reached in question 1b? Why?

3. Let’s get back to a static game. The market leader BestGames is releasing its new game for Christmas. Worried about the competition, both Game4U and All4Games

decide to commercialise their games in October or March. They face the payoff matrix below, where a is an integer.

Payoffs (Game4U, All4Games)

In £10,000

All4Gamers

October

March

Game4U

October

a,a

100,50

March

50,100

-25,-25

a. For what values of a is (October, October) a dominant strategy equilibrium – i.e. a Nash equilibrium reached through iterated elimination of dominated strategies?

b. For what values of a is (March, March) a dominant strategy equilibrium?

c. Find the (pure strategy) Nash equilibria of the game as a function of parameter a? Explain your answer.

Part B [20 points]

Richard and Judy want to give £100,000 to their children Rose and Mary. Rose is rich, single and unhappy; Mary is married with 2 young children, relatively poorer than

Rose but also happier. We will assume that the marginal utility provided by a pound declines the richer you are. Richard and Judy consider different options:

1. First they think that they should share the money and give equal amounts to each of their child. How much do Rose and Mary receive?

2. Then they consider sharing the amount by giving shares to their children proportional to the size of their families. In this scenario, the money is effectively

shared between Rose, Mary, Mary’s husband and Mary’s two children, giving an equal share to each individual. How does this work out?

3. How should they share the money if they want to provide the greatest possible collective happiness for Mary and Rose?

4. How should they divide the cash if they want to equalise happiness between the 2 sisters?

5. In your view, which option is the fairest? Explain. Is that an efficient solution in the sense of Pareto?

Part C[20 points]

John has a Cobb-Douglas utility function , where and where is football game tickets and is take-away pizzas. Suppose that John’s income is , and that the prices for

tickets and pizzas are and respectively.

1. Derive the demand functions for football game tickets and take-away pizzas. Are these goods inferior or normal? Ordinary or Giffen? Are x and y complements or

substitutes?

2. Can you explain what it means for John’s tastes and consumption levels if a=0? If a=1? If a=1/2?

Part D [30 points]

Jane is a single mum working for Brighton and Hove City Council. She has a flexible-working contract that allows her to work between 10 and 30h a week for a constant

hourly pay rate of £10 an hour. Jane is currently working 20h a week, but could change this schedule to better suit her needs.

Finn, Jane’s son, is 3 and is currently going to nursery 5 mornings a week for 3.5 hours each morning, and he spends his Wednesdays afternoon with his grandmother

Edna. The UK government subsidises childcare for up to 17.5 hours a week for every child aged 3 or 4. The subsidy takes the form of a direct transfer of £5 per hour

from the government to the childcare provider. At the nursery attended by Finn, unsubsidised childcare costs £8 per hour. Edna does not charge Jane anything to look

after her grandson, but she does not feel able to look after him for more than the 2.5 hours she already does. {Note that to simplify the problem, we assume that

Jane‘s commuting time is zero}.

1. Graphically shows Jane’s current budget line and optimal labour supply.

2. Now let’s consider some minor changes to the initial scenario:

a. Imagine that Jane’s childcare provider raise its hourly rate by 10%, explain how this will impact on the number of hours she works. Is she better or worth off in

this new equilibrium position?

b. Let’s assume now that the government is looking into different policy options to address the heavy burden of childcare on working families. For each option listed

below explain how Jane would be affected: i.e. how it would impact on her labour supply and whether she would be unambiguously better off. The options considered are:

i. To subsidise up to 25 hours of childcare per week and per child.

ii. To continue to subsidise 17.5 hours of childcare per week and per child, but offer a tax rate reduction for one working parent (either mum or dad but not both can

benefit from this). {To simplify we assume that all income is taxed at 10% for one working parent instead of 30% for everybody else.}

iii. To continue to subsidise 17.5 hours of childcare per week and per child, but also provide a weekly lump-sum transfer to one working parent of £37.50 (either mum

or dad can receive this but not both).

c. Explain the trade-offs that the government has to consider when deciding on the policy option to adopt.

End of coursework

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