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ECON 20002 Intermediate Microeconomics

Assignment

Knowledge is not power. It is the implementation of knowledge that is power. Larry Winget

Problem 1. Consumer Theory: Labour-Leisure choice and Poverty traps.

Robert is currently single, unemployed and leaving alone. He is receiving government allowance (similar to Newstart) but looking for a job. He found a job that pays $15 per hour, but he is confused how accepting the job will affect his entitlement to the government assistance. Your job is to help Robert to figure it out. (Allowance is usually per fortnight, but we will look at per day for simplicity).

a) Suppose that Robert has 16 hours a day available for work. If he doesn’t work at all, he receives $81 per day from the government (that includes $58.50 plus $22.5 value of rent assistance and health care card). He can spend these money on “other goods”, which have price equal to one. Show this point A on a diagram with leisure on horizontal axis and “other goods” on vertical, as in lecture 3.

b) If Robert earns less than $9 per day in his job, he can keep all his allowance and his earnings from the job. How many hours and minutes would it take him to earn $9? Show new point B (where he earns $9) on the same diagram as in a).

c) If Robert earns more than $9 but less than $21 per day in his job, he will lose 50c for each dollar earned between $9 and $21. For example, assume that Robert earns $13 per day. Then his government allowance will decrease by (13-9)*0.5 = $2. How long will it take Robert to earn $21? How much money is available to spend on other goods in that case? Show new point C on the diagram.

d) If Robert earns more than $21 but less than $96 per day in his job, he will lose 70c for each dollar earned between $21 and $96. That’s in addition to 50c per dollar loss for $9 to $21 range. If he earns $96, how much leisure is he enjoying? How much money is available to spend on other goods? Show this point D on the diagram.

e) If Robert works even one minute more than at point D, he will lose all government allowance (including rent assistance and health care card worth $22.50 per day). Draw his budget line when he works more than at point D.

f) Draw Robert’s overall budget curve (for all values of leisure).

g) Draw Robert’s indifference curves such that he prefers to accept full time job (8 hours per day). Show his optimal choice on a diagram.

h) Peter (who otherwise is exactly in the same situation as Robert) earns just under $96 per day from his job. Draw several Peter’s indifference curves and show his optimal choice on a diagram.

i) Mary (in similar situation to Robert and Peter) earns $19 per day from her part time work. Draw several Mary’s indifference curves and show her optimal choice on a diagram.

You answer to this question should include 3 graphs: for each of three people, you need to draw a separate graph with budget curve with all points (like kinks) identified, his/her indifference curves and his/her optimal choice. If all three graphs are correct, you will receive full mark for this question.

Econ 20002 - 2013 The Assignment A. Page 1 of 2

Problem 2. Producer Theory: Cost Minimisation.

Quick Joe uses fruits (F) and labour (L) to produce fruit juice (q). His production function is: q = min {L0.5, F/3},

where labour is measured in hours, fruits in kg, and juice in (large) bottles. For example, if he uses 3 kg of fruits and spends 1 hour, he can produce 1 bottle of juice.

a) Derive an expression for Quick Joe’s expansion path.

b) Draw the expansion path and several isoquants on a diagram with labour on horizontal axis and fruits on vertical.

c) Let the price of labour-hour be given by w = $10 and the price for each kg of fruit be given by p = $2. What is the optimal amount of labour and fruit to use to produce q bottles of juice, if Joe strives to minimise costs? Illustrate on the graph from b).

d) What is Quick Joe’s long-run total cost function?

Problem 3. Markets: Perfect Competition.

Assume that a perfectly competitive, constant cost industry is in a long run equilibrium and each firm is paying $3 tax per unit of the output. The government decides to abolish the tax.

a) Explain what would happen in the short run to the equilibrium price and industry output; number of firms in the industry; output and profit of each firm. Illustrate on diagrams for the market and a particular firm.

b) Explain what would happen in the long run to the equilibrium price and industry output; number of firms in the industry; output and profit of each firm. Illustrate on diagrams for the market and a particular firm. Compare both to the initial long run equilibrium and to the short run equilibrium.

You answer to this question should include graphs and explanations in words.

Problem 4. General equilibrium: Efficiency in the Edgeworth box.

Boon Han and David always eat miso soup and sushi in exact proportions – one miso per one sushi. They throw away any extra soup or sushi as it would not give them any pleasure. Once, they were stuck in the office together for hours, marking students’ assignments. Boon Han had 2 miso soups and 10 sushi with him; David had 12 miso and 3 sushi.

(For the purpose of this question, assume that miso and sushi can be divided into little pieces so one-half miso or one-hundredth of sushi makes sense)

a) Draw the Edgeworth box for Boon Han and David. Please put Boon Han at the origin and David “upside down”; put miso on horizontal axis and sushi on vertical. Show their endowment point.

b) Show all Pareto optimal allocations of miso and sushi between Boon Han and David in the Edgeworth Box. Please note that this question is a bit tricky, though not difficult. Draw a bunch of indifference curves and look for tangencies.

You answer to this question should include the Edgeworth box with it size shown and all Pareto optimal allocations clearly identified

Bonus question (for 0.5 point). Joke competition – see LMS for details.

Econ 20002 - 2013 The Assignment A. Page 2 of 2

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