Economics 713: Assignment 3-

Q1. When people eat dinner together at a restaurant they might either agree that each person will pay his own bill (plan A), or else that each will pay an equal share of the total bill (plan B). Suppose three people with identical preferences and incomes eat at a restaurant where the price of food is $6 a pound.

(a) Draw diagrams showing the budget constraints implied by plans A and B, from the point of view of one person.

(b) Suppose each person is selfish (i.e., interested only in his own utility, not anyone else's). Use indifference curve analysis to determine whether more food will be consumed under plan A or plan B.

Q2. State whether the following assertion is true, false or ambiguous, and explain why.

"There are many firms which produce wooden chairs, and many firms which produce wooden tables. If these firms are all separate, and if they all maximize profits, taking prices as given, then the equilibrium cannot be efficient. This is because when the chair firms increase output they bid up the price of wood, which reduces the profits of the table-producing firms. But the chair firms ignore the effect of their output decisions on the profits of the table firms. An efficient equilibrium would be achieved if all of the firms produced both tables and chairs."

Q3. Consider a simple economy in which there are just two occupations, coal mining and auto repair. The mining and auto repair industries are perfectly competitive, and they happen to have identical labor demand curves, given by w = 400 - L, where w is the daily wage (net of any training costs borne by workers), and L is the number of workers employed in the industry.

There are 420 workers in the economy, 294 men and 126 women, all equally productive in both jobs. All workers prefer auto repair work to coal mining, but the extent of this preference varies from one worker to another. The distribution of equalizing differences over workers is uniform between 0 and $42. Sex and occupational preferences are independently distributed.

a. Find the equilibrium wage differential and occupational distribution for this economy.

b. Suppose Fred is an "average" worker, who considers the equalizing differential to be $21 a day. Does Fred gain or lose from the diversity of preferences in the economy? That is, would Fred be better or worse off if everyone else in the economy had the same preferences as he does?

c. Suppose that women are excluded from coal mining jobs. How will this affect the equilibrium? What will happen to the average wages of men and women? Who will gain under this restriction, and who will lose?

d. Suppose that employers who have excluded women are found liable for damages. How would you compute the damages?

e. Does it make sense to interpret the exclusion of women from mining jobs as rational exploitation of the minority by the majority?

Q4. Let F and G be distribution functions defined on the real interval [a,b], with density functions f and g.

a. Can you find an example in which F and G are ordered in the sense of first-order stochastic dominance, but the likelihood ratio is not monotonic? If you can't find such an example, can you prove that no one else can find one either?

b. Can you find an example in which the likelihood ratio is monotonic, but F and G are not ordered in the sense of first-order stochastic dominance? If you can't find such an example, can you prove that no one else can find one either?