Economics 311 Midterm Exam
Q1. A consumer has an income of $300 per week, which is spent entirely on two goods, food (f), measured in pounds, and gas (g), measured in gallons. The consumer's utility function is
u(f, g) = √(f/100) + log (g)
(a) If the price of food is $1 per pound, and the price of gas is $4 per gallon, what is the optimal consumption plan?
(b) If the price of gas rises to $10 per gallon, does the consumer buy more food?
Q2. Consider a two-person, two-good exchange economy, in which the consumers' utility functions are given by
u1(x, y) = log (x) + log (y)
u2(x, y) = 2 log (x) + log (y)
where x is the amount of the first good consumed, and y is the amount of the second good consumed. Consumer 1 is endowed with 1 unit of x and zero units of y, and consumer 2 is endowed with 1 unit of y and zero units of x.
(a) Find the set of Pareto optimal allocations.
(b) Find a competitive equilibrium, and determine whether it is Pareto optimal.
(c) Does the first welfare theorem hold for this economy?
Q3. A worker is searching for a job that will last two years (no matter how long it takes to find it). Each month, the worker receives exactly one job offer, and the cost of job search for a month is $800. The best possible job pays $40, 000 a year, the worst pays $20, 000, and any wage between these extremes is equally likely (e.g. there is a 60% chance that any given job pays at least $28, 000).
(a) What search strategy would maximize the expected wage, net of search costs?
(b) If an unemployment benefit of $600 per month is available while the search continues, what happens to the average search duration?