## Question from Past Microeconomics Qualifying Exam

Spring 2001 - Section II, Question three, George Mason University Give complete answers to three of the following four questions (about 25percent each) Write clear concise and legible answers.:

Suppose Al has the utility function ${\displaystyle U = u(X~1, X~2) }$, where ${\displaystyle X~1}$ and ${\displaystyle X~2}$ are goods. His income is ${\displaystyle W}$ dollars. The prices of ${\displaystyle X~1}$ and ${\displaystyle X~2}$ are ${\displaystyle P~1}$ and ${\displaystyle P~2}$ respecitively.

• a. Derive Al's demand for ${\displaystyle X~1}$. Be sure to explain your reasoning and mathematics
• b. Determine wheather Al's demand for ${\displaystyle X~1}$ is downward sloping or not. Be sure to explain your reasoning and mathematics.
• c. Determine whether ${\displaystyle X~1}$ is a normal good or not. Be sure to explain your reasoning and mathematics.
• d. What is the relationship between the demand for good ${\displaystyle X~1}$ and the excess demand for good ${\displaystyle X~1}$? If lambda (L) appeared in your calculations, what is its economic interpretation?