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ECC2000/ECC5900/BEX5900

Intermediate microeconomics

Tutorial 2

Submission procedure:

● Browse and upload an electronic copy of your document in ONE PDF file—do not paste text or images.

● Name the file as “xxx tutorial_2” where “xxx” is your student ID.

● You can submit a scanned copy of your handwritten solutions if you like.

● Late submissions will not receive credit.

● It is not necessary for your answers to be correct to receive credit; you need to show effort in attempting the questions.

1   Budget

A consumer buys water and gasoline. His income is $100. Water costs $1 per gallon, while gasoline costs $2 per gallon.

1. With water on the vertical axis and gasoline on the horizontal axis, sketch the consumer’s budget line. Label the intercepts.

2. Illustrate the impact of a subsidy that reduces gasoline prices.

3. Illustrate the impact of an income tax that reduces the consumer’s income.

2   Budget Lines

On the graph below, draw a budget line for each case.

1. p1 = 1, p2 = 1, m = 15 (use blue ink. m is the income.)

2. p1 = 1, p2 = 2, m = 20 (use red ink)

3. p1 = 0, p2 = 1, m = 10 (use black ink)

4. p1 = p2, m = 10p1 (use black ink to draw a dashed line.)

3   Three Goods

In a small country near the Narrow Sea, there are only three commodities: potatoes, meatballs, and jam. Prices have been remarkably stable for the last 50 years or so. Potatoes cost 2 dragons per sack, meatballs cost 4 dragons per crock, and jam costs 6 dragons per jar.

1. Write down a budget equation for a citizen named Gendry who has an income of 360 dragons per year. Let P stand for the number of sacks of potatoes, M for the number of crocks of meatballs, and J for the number of jars of jam consumed by Gendry in a year.

2. The citizens of this country are in general very clever people, but they are not good at multiplying by 2. This made shopping for potatoes excruciatingly difficult for many citizens. Therefore it was decided to introduce a new unit of currency, stags, such that potatoes would be the numeraire. A sack of potatoes costs one unit of the new currency while the same relative prices apply as in the past. In terms of the new currency, what is the price of meatballs?

3. In terms of the new currency, what is the price of jam?

4. What would Gendry’s income in the new currency have to be for him to be exactly able to afford the same commodity bundles that he could afford before the change?

5. Write down Gendry’s new budget equation.

6. Is Gendry’s budget set any different than it was before the change? Why?

4   Advertisement

This question is optional for ECC2000, although I highly recommend you to try it. It is manda-tory for ECC5900.

Petyr has $5,000 to spend on advertising a new kind of dehydrated sushi. Market research shows that the people most likely to buy this new product are recent recipients of M.B.A. degrees and lawyers who own hot tubs. Petyr is considering advertising in two publications, a boring business magazine and a trendy consumer publication for people who wish they lived in Melbourne.

Fact 1: Ads in the boring business magazine cost $500 each and ads in the consumer magazine cost $250 each.

Fact 2: Each ad in the business magazine will be read by 1,000 recent M.B.A.’s and 300 lawyers with hot tubs.

Fact 3: Each ad in the consumer publication will be read by 300 recent M.B.A.’s and 250 lawyers who own hot tubs.

Fact 4: Nobody reads more than one ad, and nobody who reads one magazine reads the other.

1. If Petyr spends his entire advertising budget on the business publication, his ad will be read by ____ recent M.B.A.’s and by ____ lawyers with hot tubs.

2. If he spends his entire advertising budget on the consumer publication, his ad will be read by ____ recent M.B.A.’s and by ____ lawyers with hot tubs.

3. Suppose he spent half of his advertising budget on each publication. His ad would be read by ____ recent M.B.A.’s and by ____ lawyers with hot tubs.

4. Draw a “budget line” showing the combinations of number of readings by recent M.B.A.’s and by lawyers with hot tubs that he can obtain if he spends his entire advertising budget. Does this line extend all the way to the axes? ____ Sketch, shade in, and label the budget set, which includes all the combinations of MBA’s and lawyers he can reach if he spends no more than his budget. Assume free disposal.

5. Let M stand for the number of instances of an ad being read by an M.B.A. and L stand for the number of instances of an ad being read by a lawyer. This budget line is a line segment that lies on the line with equation ________. With a fixed advertising budget, how many readings by M.B.A.’s must he sacrifice to get an additional reading by a lawyer with a hot tub? ____

5   Marginal utility

A consumer’s marginal utility from a DVD is 10 and his marginal utility from a CD is 5. How should he reallocate his expenditures if the price of a DVD is $15 and the price of a CD is $10?

6   Perfect substitute

Tywin wants to buy some toilet paper. He has $6 to spend on either Kleenex (represented by K) or Sorbent (represented by S). His utility can be approximated by U (K, S) = 2K + S.

1. Draw and label Tywin’s indifference curves for U = 4 and U = 6.

2. Assume the price per role is $3 for Kleenex and $2 for Sorbent. Draw Tywin’s budget constraint and determine the optimal quantity of K and S.

3. Now assume the Sorbent is on sale, offering 50% off. Draw Tywin’s new budget constraint and determine the optimal quantity of K and S.

4. Following Sorbent’s promotion, Kleenex offers one-third off, lowering the price to $2 per roll. What is Tywin’s optimal quantity of K and S now?

7   Derivatives

This course involves quite a bit calculus. Here are some practice. The following exercises are part of the tutorial questions, so please finish them as well.

Appendix

The appendix is for reference only. The tutor will not go through this explicitly during the online tutorial.

A   Rules for Calculating Derivatives

There are straightforward rules for calculating the derivatives of the functions we will work with in this class.