## Question from Past Microeconomics Qualifying Exam

Fall 2000 - Section II, Question one, George Mason University Suppose that automobile size (weight) and gasoline are inputs into the household production of transport services, ${\displaystyle T = t(S,G) }$, with ${\displaystyle T}$ increasing as ${\displaystyle G}$ increases but decreasing as ${\displaystyle S}$ increases. Suppose also that travel is a bit risky, and that the probability of an accident increases with travel, ${\displaystyle P = p(T) }$, while the damage generated falls as automobile size increases, ${\displaystyle H = Ho - d(S) }$, other things being equal. If no accidents occur damages equal zero e. g. ${\displaystyle H = Ho }$. Assume that individuals value only health, ${\displaystyle H}$, transport services, ${\displaystyle T}$, and other consumption, ${\displaystyle C}$.

• a. Characterize a typical person's (Al's) expected utility maximizing automobile size (Assume that Al has ${\displaystyle W}$ dollars to allocate between ${\displaystyle C,S, }$ and ${\displaystyle G}$ which are purchased in competitive markets). Explain the economics behind the mathematics that characterize Al's optimum.
• b. Characterize Al's demand function for automobile size.
• c. Does Al's short run demand for gasoline necessarily slope downward when Al's utility function is separable and strictly concave? Briefly explain your analysis.