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UNIVERSITY OF CALIFORNIA, RIVERSIDEDEPARTMENT OF ECONOMICSSpring 2011

Maithili Ramachandran

ECON 102: INTERMEDIATE MICROECONOMICS

PRACTICE PROBLEMS for the FIRST MIDTERM EXAM

Instructions you will read on the cover page of the test 1

1. Write your full name and student ID in the space indicated below.

2.

Circle the name of your Teaching Assistant. Your discussion section # is not required.3. This exam is for 50 points. It contains 7 pages and 4 questions.

4. You will have 50 minutes from 3:10 to 4:00pm to complete the test.

5. Cheating gets you a zero and an F.

6. Present your work with care: draw neat and fully-labelled diagrams, show yourcomputation and proofs in full and be legible in your writing.

Last Name, First Name: ______________________________________________________

Student ID: ______________________________________________________

Teaching Assistant: Anca Sirbu Jacob Kevari

Sarah Daway Sheetal Bharat

For TAs use only:

Question1

Question2

Question3

Question4

Total

1 Practise with instruction #6 in mind and it will serve you well on the test.

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1. Suppose you had the utility function u(x 1, x2, x3, x4) = x 10.4 x20.2 x30.2 x40.2 and you had$100 to spend on these four goods. How much should you spend on good 1 to maximiseyour utility?

2. Suppose you had the utility function u(x 1, x2) = x1-1 x2. Draw the indifference curvescorresponding to utility levels of 10, 20 and 30. What does the shape of these indifferencecurves tell you about the nature of the two goods?

3. Gwyneth is a travelling enthusiast. She saves up every year so she can take a vacationabroad for at least a week. This year she is going to Scandinavia for a month so she plansto buy new boots and gloves. The boots she likes cost $149 a pair; the gloves are $13each.(a) If she likes to have twice as many pairs of gloves as boots, how many of each will she

buy with a budget of $350?

(b) What kind of preferences does Gwyneth seem to have for the two goods she isbuying?

4. Denholm is the head of the largest IT company in the UK, a fact he prides himself ongreatly. He is not very involved with the business these days though, preferring to occupyhimself with selecting striped ties and beer mugs. Denholms preferences for ties (T) andmugs (M) follows the utility function u(T, M) = 17T + 29M. The price of any tie is $17and a mug costs $29.(a) Denholm spent $1972 on ties or mugs in the last year. If he had been maximising his

utility, how many striped ties and beer mugs would he have bought?

(b) The price of mugs has halved this year and Denholm plans to spend only $493 onmugs or ties. What is his optimal bundle now?

(c) What kind of preferences does Denholm exhibit for ties and mugs?

5. Robin sets aside $1000 each month for food (x 1) and gasoline (x 2). Gas is $2.50 a gallonand food is $19 per unit. Robins demand for gasoline is given by x2 = 0.05m/p 2.(a) Compute Robins consumption of food and gas.(b) If gasoline is subsidized at the rate of 50 cents per gallon, how does Robin adjust her

consumption of food and gas?(c) Did Robins expenditure on food change as a result of the gas subsidy? Does it

change if instead of a subsidy, a tax of $1.50 per gallon was placed on gasoline?(d) Bonus: What can you infer about Robins demand for food? (i.e. do you think it is

influenced by the price of gasoline?)

6. Show why indifference curves cannot cross.

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7. Fred has a monthly income of $1800. Each month he orders small pizzas at the price of $11 each, books from Amazon.com at the price of $32.56 each and DVDs fromBlockbuster at $0.99.Suppose his consumption of pizzas, books and DVDs is lumped into one composite goodcalled X 1. Let the price of the composite good, p 1 simply be the sum of the three unitprices above.His city sets the water rate at $3 per 750 gallons. Denote Freds water consumption ingallons by x 2.Freds demand for the composite good is given by x1 = 0.99m/p 1.

(a) In a given month, how many gallons of water does Fred use? How many units of thecomposite good does he consume?

(b) His city council decides to tax water consumption at the flat rate of $2 for every 750gallons. How does this change Freds water use?

(c) If an income tax was levied on Fred such that the city collects the same tax revenuefrom Fred as the flat rate, what would it be?

(d) If Fred paid this amount as income tax, what is his optimal bundle now?(e) Will Fred vote for the city council to levy the quantity tax or the income tax? Explain.

8. Calculate the marginal rate of substitution in each of the following functions:

(a) u(x1, x2) = min.{x 1, x2}(b) u(x1, x2) = 3x 1 + ln(x 2)(c) u(x1, x2) = 5x 1 x2 (d) u(x1, x2) = x1 + 4x2

9. In the following cases, identify the utility functions that violate the assumption of monotonicity, convexity or both:

(a) u(x1, x2) = max.{2x 1, x2}(b) u(x1, x2) = (x 1 + x2)2

(c) u(x1, x2) = x1 + ln(x2)

10. What is the name of your Teaching Assistant?