(econ198)[2006](s)midterm~masze^_10231.pdf

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Department of Economics, HKUST Department of Economics, HKUST

ECON 198 ECON 198

MICROECONOMIC THEORY I MICROECONOMIC THEORY I

Semester: Spring 2006 Semester: Spring 2006

Prof. S. F. Leung Prof. S. F. Leung

Midterm Examination Midterm Examination

March 28, 2006 March 28, 2006

3:00 pm C 4:20 pm 3:00 pm C 4:20 pm

This is a closed book examination. You have 80 minutes to complete the test. Write coherently, lucidly, and legibly. Always explain your answerThis is a closed book examination. You have 80 minutes to complete the test. Write coherently, lucidly, and legibly. Always explain your answer. The maximum score for this exam is 80 points. Points are marked next to the questions and may be served as a rough guide to how much time you should allocate on each question. Points will be deducted for irrelevant materials. Use mathematics and/or diagrams wherever appropriate to support your answer.

1. (5)

Suppose there is an increase in the income tax rate. Under what conditions will a worker increase his/her hours of work? Use indifference curve analysis to support your answer.

2. (5)

The Financial Secretary Henry Tang has just proposed in his 2006 Budget that the HKSAR government will provide short-term travel support on a trial basis for Tin Shui Wai, Tung Chung and North District residents who are financially needy and have completed full-time courses with the Employees Retraining Board. This will encourage unemployed people in districts further afield who are not receiving CSSA to take up employment. Will the travel support scheme encourage the unemployed to take up employment? Use indifference curve analysis to support your answer.

3. (5)

A consumer ranks different bundles (x,y) of goods x and y in the following way:

(a) Bundle (1,3) is preferred to bundle (3,1).

(b) Bundle (4,8) is indifferent to bundle (8,4).

(c) Bundle (2,6) is indifferent to bundle (10,5).

Does this consumers ranking satisfy the fundamental axioms of preferences? Explain.

4. (5)

Determine whether V(x,y) is a monotonic transformation of U(x,y) and explain your answer.

(a) U(x,y) = 4xy + 7, V(x,y) = 3(x)1/2(y)1/2 ,

(b) U(x,y) = 5xy + 8, V(x,y) = 5x(y + 8)

5. (16)

Consider the utility function and the budget constraint , where . Answer the following and show your derivations.

(a) (2) Is the utility function quasi-linear? Prove or disprove.

(b) (2) Is the utility function homothetic? Prove or disprove.

(c) (2) Does the utility function exhibit DMRS? Prove or disprove.

(d) (2) Let x* and y* denote the optimal consumption of x and y. Calculate x* and y*.

(e) (2) Is .x*/.a > 0? Give an intuitive interpretation of this result.

(f) (2) Are x and y normal, inferior, or Giffen goods? Explain.

(g) (2) Are the demand curves for x and y homogeneous