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Australian National University

IDEC8029 ISSUES IN APPLIED MICROECONOMICS

Mid-Semester Exam

Semester 1, Friday 4 April 2014

Writing period: 60 Minutes duration

Study period: 15 Minutes duration

Permitted materials: Non-programmable Calculators

You must attempt to answer all questions.

This exam has 100 marks in total.

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Section A State whether each of the following statements in italics is TRUE or FALSE or Uncertain, and briefly (1-3 sentences, and a graph or some maths if needed) explain your reasoning as clearly and well as you can. [5 marks each; 35 marks in total]

(1) Billie has asked her daughter, Jill, to make sure her room is tidy before guests come. Jill may leave her room Tidy, Untidy or Very Untidy. Billie says that she will be Angry if her room is not tidy but she may also be Supportive or she may punish Jill (Punish).

Billie

Jill

Angry Supportive Punish

Tidy -5,-5 6,6 -5,-5

Untidy 5,5 3,1 4,5

Very Untidy 8,5 10,0 2,6

This game is only played once and is played sequentially with Jill the first player and her action is observable to Billie. The outcome will be that Jill will play Untidy and Billie will play Punish.

(2) In the diagram below, the indifference curves cannot represent the preferences of a risk averse person.

(3) Consider the following diagram that shows two bundles of contingent consumption: Bundle A (Cg

A , CbA) and Bundle B (Cg

B , CbB), where the subscript g refers to the Good

state of the world and the subscript b refers to the Bad state of the world. There are only two states of the world (and both cannot occur at the same time). Assume that the diagram is drawn to scale. If Roger is indifferent between Bundle A and Bundle B then Roger must believe that the probability of the Bad state of the world occurring is higher than the probability of the Good state of the world occurring.

(4) Suppose there are two possible states of the world: good and bad. Let expected utility be given by:

(Equation 1) V = U(Cg)+(1- )U(Cb),

where Cg is consumption in the good state, Cb is consumption in the bad state, and is the probability of the good state occurring. For consistency assume for the purpose of the questions below that Cg is measured along the horizontal axis.

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(a) Use Equation 1 to derive the following formula for the marginal rate of substitution

- MRS =

|

=0

= U()

(1 )U()

(b) Derive an expression for the slope of the fair odds line.

(c) Based on the MRS formula, the MRS is a function of the slope of the fair odds line. Use a diagram to show that a person's indifference curve will vary as the slope of the fair odds line changes.

(d) Explain why a risk averse persons indifference curves are tangent to the fair odds line along the 45 degree ray from the origin.

(2) Luke has $100 and is presented with an option to invest in a business called Pigs vs Birds software Co. that is developing a software program called Angry Pigs. If the business is successful, the business owners have promised him a payment of $5 for every $1 he invests but he loses his investment if the business is unsuccessful. Suppose that Lukes utility function is given by U(C)=ln(C) and that the investment only has a 25% chance of being successful. He may invest up to $100 in the business.

(a) Draw a diagram (with Lukes consumption contingent on the business being successful Cg on the horizontal axis) that shows the fair odds line of the investment, his budget constraint over contingent consumption, and indifference curves. Indicate his utility maximizing bundle of contingent consumption.

(b) Equate the MRS to minus the slope of the budget constraint and solve for the ratio of Cg and Cb. For any investment level Y, Luke's contingent consumption is Cg = 100+5Y and Cb =100-Y. Use this information to solve for the level of investment that maximises Luke's expected utility.

(c) Suppose that Pigs vs Birds Software Co. has the idea of renaming its software to "Angry Birds" which raises the chance of success to 1/3. Show the impact of this change on Luke's indifference curves and his optimal level of investment. Calculate Y*.

(3) Patel is doctor who has a current wealth of $100 but faces a 50% chance of being successfully sued for negligence in which case he would incur a loss of $40. Patel's utility is given by U = ln(C). Patel has the option of purchasing insurance at a rate of 0.6 per unit (in the event of being successfully sued Patel receives a payout of $1 for every unit of insurance).

(a) Draw a diagram with shows Patel's budget constraint over contingent commodities (with consumption in the event of not being successfully sued on the horizontal axis). Find the value of the certainty equivalent and his expected wealth in the event he does not have insurance and indicate these values on the diagram.

(b) Find the amount of insurance that maximises Patel's utility and indicate the associated contingent consumption on the diagram. Is he fully insured?

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(c) Suppose that Patel has become a very bad doctor over time and that the probability of being successfully sued is now 60%. Show the effect of this change on a diagram (the same one as before if you wish) and calculate the optimal amount of insurance for Patel.