ECON7030 MICROECONOMIC ANALYSIS

MOCK PROBLEM SET 2

Instruction:

This is an open-book problem set. You are NOT ALLOWED to discuss the problem set and/ or the answers with anyone else.  You can do your own research to find the answers. If your answers are based on a reference, you MUST properly CITE the source of such reference.  The use of AI to develop responses is prohibited and may constitute student misconduct under the Student Code of Conduct.

You have 24 hours to complete AND submit your answers by the due time.  Hand- written as well as typed answers are welcome. Make sure that you upload a single PDF file containing multiple pages. Submit on time, ideally at least 1 hour in advance of the deadline. It shows competence and professionalism, and it will ensure that you avoid late penalties.

Answer all questions. Justify all your answers. Every graph (figure or diagram) in your answers has to be well-labelled.  For functions that intersect the axis, the points where they intersect them must be identified (providing the corresponding numbers). All quantities of goods can be treated as continuous variables unless explicitly stated otherwise. Show your work.

Question 1 True, False, or Uncertain? Justify your answers.

(a) (5 marks) Inflation and the rising cost of living are currently a big problem. Suppose that the prices of all the goods in your consumption bundle increase at the same rate of 5%. The Union negotiated a nominal salary increase of the same rate, 5%. You are equally well of.

(b) (5 marks) Tom consumes only two goods, X  and Y.  He spends 40% of his income in X . Tom’s income elasticity of demand for X is β, where β > 0. Tom’s (Marshal- lian) demand for X  has a price elasticity equal to -0.4β .  X and Y are perfect complements for Tom. [Hint: Slutsky equation.]

(c) (5 marks) John has monotonic preferences for two goods, X  and Y.  The price of Y is one dollar per unit.  The following diagram illustrates one of his indiference curves, labelled U0 .  It also shows two budget lines corresponding to income levels M and M, , respectively, while the prices of X and Y remain constant. A = (xA , yA ) is the optimal bundle when the income is M. When the income changes to M, , ceteris paribus, John’s new optimal bundle(s) must be located along the blue section.

(d) (5 marks) Bob consumes only two goods, X and Y. Consider the price combinations A, B and C, in the following table.  Bob’s chosen bundle in each situation is also shown in the table. Bob’s preference satisfies both WARP and SARP.

Situation Px     Py     X   Y

p: per-unit price of insurance, π: probability of accident,

L: loss wealth from the accident

X: amount of purchased insurance.

An insurance purchaser is an expected utility maximiser.  The insurance is unfair in favour of the insurance company; that is, the per-unit premium is higher than the probability of insurance payout, p > π . The insurance model suggests that risk-averse consumers choose to be fully insured, i.e, X = L.

Question 2 The 2022 Australia Federal election is just around the corner. The compe- tition between the two candidates, Scoot Morris and Antone Alba, is fierce.

As a consumer (and Australian voter), you only care about public transportation and child care. Let public transportation be good X and child care be good Y. Each trip in the public transportation costs $10 and each day of child care service costs $100.  Your after-tax income is $500 per week. Assume that you always consume a positive amount of both X and Y (also known as interior bundles). Your utility function is given by:

U (x, y) = Qxβ + 2y + 1,

where Q > 0 and 0 < β < 1.

(a) (5 marks) Write down the MRS in terms of Q,  β,  x,  and y.

(b) (5 marks) Draw two indiference curves.  Do the indiference curves have the same

slope along any vertical line (when x is held constant)? Illustrate and explain.

(c) (2 marks) Is it possible to establish whether Y is a normal or inferior good? Explain.

(d) (5 marks) Based on your answer in part (c), is the price elasticity of Hicksian demand for Y greater, smaller, or equal to that of Marshallian demand? Explain. DO NOT derive the Hicksian and Marshallian demand functions for Y.

(e) Scoot Morris promises an income tax reduction that increases you after-tax weekly income by 10%, from $500 to $550.

(i) (2 mark) Without solving the utility maximisation problem, establish how your consumption of X and Y will change. Justify.

(ii) (4  marks) Find the optimal consumption bundles with and without this tax reduction.

(f) Now consider Antone Alba’s campaign instead. He promises to reduce the child care cost by 10%.

(i) (2 mark) Without solving the utility maximisation problem, establish how your consumption of X and Y will change. Justify.

(ii) (2 marks) Find the optimal consumption bundle with the reduced cost of child care.

(iii) (5 marks) With a well-labeled diagram, illustrate the Hicksian decomposition of the price efect of Antone’s campaign into the substitution efect and the income efect. Do not forget to explain and label the diagram.

(g) (5 marks) Now assume that Q = 1 and β  = 0.2, who should win your vote, Scoot Morris or Antone Alba?  If you are indiferent between the two, choose a “silent” vote.  Show and explain only within the context of your previous answers and the given information available. Please do not assert your personal political views here.

(h) Your sister, Josephine, is also an eligible voter who faces the same dilemma.  She earns the same as you. However, we do not know her utility function.

(i) (5 marks)  During the family gathering on ANZAC day, Josephine indicated that, if Scoot Morris wins, she will choose the bundle S = (3, 5.2).  Assume that Josephine’s preferences satisfy WARP. Draw the set of possible bundles that Josephine may choose from if Antone wins. Call this set W. REDRAW the diagram only with the budget lines under Scoot’s and Antone’s campaigns. Illustrate the set W in this new diagram.

(ii) (5 marks) Unlike you, Josephine has never taken ECON7030. She then revealed that if Antone Alba wins, she will choose bundle A= (4, 5.1).  Do Josephine’s revealed preferences satisfy WARP? Explain and/or illustrate your answer.

(iii) (3 marks) Given Josephine’s revealed preferences of bundle S=(3, 5.2) if Scoot wins and bundle A=(4, 5.1) if Antone wins, can you predict who would win Josephine’s vote? Explain.

Question 3 Justin is currently working full time and earns $50,000. If he is promoted, he would earn $80,000.  Right now his chance of being promoted is 30%.  He considers getting a master degree in Economics to help improving his chance of being promoted. Suppose, there is 5% chance that he would fail to complete the degree. Without this degree, his chance of being promoted remains at 30%. However, if he gets the degree, the chance to be promoted will increase to 80%. Justin is an expected utility maximiser and his utility function over the non-negative wealth, w, is given by:

u(w) = √w

(a) (5 marks) Is Justin risk-averse, risk-neutral, or risk-seeking? Show your work.

(b) (5 marks) Compute Justin’s expected utility if he chooses not to enrol in the Master program.

(c) (5 marks) Assume that the Master program is fully subsidized, i.e., it is free. Com- pute Justin’s expected utility if he chooses to enrol in the Master program.

(d) (5 marks) Now assume that the program is not free, what is the maximum fee, F , that Justin is willing to pay to enrol in the Master program? [Hint: Set up the equality and use any program or software to find the value F that solves the equation.  For example, https://www.wolframalpha.com/calculators/equation-solver-calculator]

(e) (5 marks) Suppose now that the price of the master program is F = $15, 000 and, upon being promoted, Justin’s new salary would be wp.  Find the minimum salary wp   for which Justin enrols in the Master program.  [Hint: Set up the equation and use any program or software to find wp  that solves the equation. For example, https://www.wolframalpha.com/calculators/equation-solver-calculator]