=========================preview======================
(ECON198)[2010](s)midterm~ma_wxx^_10232.pdf
Back to ECON198 Login to download
======================================================
Department of Economics, HKUST
ECON 198
MICROECONOMIC THEORY I

Semester: Spring 2010 Prof. S. F. Leung

Midterm Examination
March 30, 2010
10:30 am C 11:50 am

This is a closed book examination. You have 80 minutes to complete the test. Write coherently, lucidly, and legibly. Unless otherwise indicated, explain your answers wherever necessary. 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.
Unless stated otherwise, assume that indifference curves are strictly convex.
This exam contains 4 pages and 11 questions.
1.
(4)

If preferences are not transitive, what will happen to the shape of the indifference curves? Explain.

2.
(4)


ab ab
Is Vxy (, ) = (x+1) ( y+1) a monotonic transformation of the utility function Uxy,) = xy?
( Prove or disprove.
3.
(5)

Assume that there are only two goods X and Y. If the utility function is quasi-linear, then the demand curves for X and Y must be downward sloping. Prove or disprove by using indifference curves diagrams (i.e., do not use mathematical proofs).

4.
(5)


Assume that there are only two goods X and Y. Peter and Paul face the same prices Pxand Py. To maximize utility, Peter consumes (,xy) and Paul consumes xy).
(,
11 22
Although (,xy) may not be the same as xy) , Peters marginal rate of substitution at
(,
11 22
(,) (,xy) . The market
xy must be equal to Pauls marginal rate of substitution at
11 22 mechanism equalizes the marginal rate of substitution across different people. Prove or disprove.
5. (6)
Assume that there are only two goods X and Y. Let Idenote income. Are the following proper demand curves? Explain.
II
x=
and y= P+ PP P+ PP

xxy yxy
6.
(5)

Suppose there are only two goods X and Y, X is a normal good, and Y is an inferior good. Can they ever be gross complements? Explain.

7.
(4)


Consider the following two statements:
Statement I: An increase in the price of apples will reduce the demand for apples.
Statement II: An increase in the demand for apples will increase the price of apples.
Is there anything wrong with these two statements? Can you reconcile the apparent contradiction between the two statements? Explain.
8.
(4)

Suppose the price of a Big Mac is $10. Jonathan is in the habit of buying a Big Mac from McDonalds every Friday evening. One Friday evening, however, McDonalds raises the price of the Big Mac to $30. Upon seeing this, Jonathan is extremely disappointed. He complains to his rich uncle about the higher price of his favorite burger and that he is no longer able to afford it. His uncle, taking pity on him, decides to give him $20 so he can still afford the Big Mac. Will Jonathan buy the Big Mac? Is he bet