QUEEN=S UNIVERSITY

DEPARTMENT OF ECONOMICS

Microeconomic Theory I (Econ 212), Spring 2000

MIDTERM EXAMINATION

Instructor: Dr. Alok Ray Full Marks: 50

Time Allowed: 90 minutes

General Instruction:

This is a closed book exam. Programmable calculators, books and notes are not allowed.

Write answers in the test booklet.

Answer all questions.

Answers should be precise. Irrelevancies will be penalized.

Make sure to write your name, student ID and course number clearly in the booklet.

1. Samson consumes only bread and chickens. When the price of bread was 10 crowns per bag and the price of chickens was 6 crowns per dozen, he spent his entire income to buy 8 bags of bread and 12 dozens of chickens per month. Now, the government decides to subsidize bread and tax chickens. Consumers get a subsidy of 6 crowns for each bag of bread and they have to pay a tax of 2 crowns per dozen of chickens consumed. In addition, the government imposes an income tax. Samson=s pre-tax income remains the same but he pays an income tax of 30 crowns each month. If b be the number of bags of bread and c is the number of dozens of chickens, what is Samson=s NEW budget equation?

[4 marks]

2. For each of the following possible utility functions over two goods X and Y, indicate whether each commodity is a good, a bad or a neutral commodity (x and y are the amounts of the two goods consumed): [2x3=6 marks]

a) U= x.y

b) U= x/y

c) U=2xy/y

3. Jane lives in a dormitory that offers soft drinks and chips for sales in vending machines. Her utility function is U= 3SC (where S is the number of soft drinks per week and C is the number of bags of chips per week). Soft drinks are priced at $0.50 each, chips $0.25 per bag.

a) Write an expression for Jane=s marginal rate of substitution (MRS) between soft drinks and chips. [2 marks]

b) Use the expression generated in part (a) to determine Jane=s optimal mix of soft drinks and chips. [Hint: use the MRS condition] [4 marks]

c) If Jane has $5.00 per week to spend on chips and soft drinks, how many of each should she purchase each week? [6 marks]

4. Suppose that Natasha=s utility function is given by U(I) = I^0.5 where I represents annual income in thousands of dollars.

a) Is Natasha risk-loving, risk-neutral or risk-averse? Explain. [4 marks]

b) Suppose that Natasha is currently earning an income of $10,000 (I=10) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a0.5 probability of earning $16,000 and a 0.5 probability of earning $5,000. Should she take the new job? [5 marks]

c) Given the information in (b) above, would Natasha be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance? Give your answer to the nearest dollar. [Hint: calculate the certainty equivalent of the gamble].

[5 marks]

5. Bank 1 offers a deal on deposits of $1000 or more. You must leave your money in the bank for 3 years but Bank 1 will pay you 8% interest for the first year, 8% interest for the second year and for the third year it will pay 11% interest. In response, Bank 2 offers a deal that it clams is even better. It also requires you to deposit at least $1000 and to leave it in the bank for 3 years but it will pay 11% interest for the first year and then 8% in the second and third years. After 3 years, you can take your money out of either bank and do what you want with it. Both banks compound interest annually. Do you think that Bank 2's claim of offering a better deal is justified? Explain your answer. [6 marks]

6. Mr. Brown, the owner of a small factory, offers a higher wage for overtime work to his employees. Mr. Brown=s son, an economics undergrad student, tells his father that this may induce the employees to work less, depending on the relative strengths of income and substitution effects. Has Mr. Brown=s son mastered his Econ-212 course well? Explain your answer, using diagrams if necessary. [8 marks]