ROY MODEL

Suppose that there are two occupations in an isolated village: mechanics and stenographers. Mechanics produce cars, A, and stenographers produce memos, B. Workers are free to choose to be a mechanic or a stenographer, but cannot be both or neither. Workers are born with ability that cannot be augmented by human capital investment. Their mechanic ability and their stenography ability may differ. Their income from making cars or writing memos depends on their mechanic and stenography abilities, respectively. Workers choose the occupation that gives them higher income.

The income of a mechanic is determined by: I_A = p_AA

where p_A is the price of each car. A, the number of car produced, is mechanic ability.

The income of a stenographer is determined by: I_B = p_BB

where p_B is the price of a memo. B, the number of memos written, is stenography ability.

a) Graph the equal income line with A, the number of cars produced, on the y-axis, and B, the number of memos produced, on the x-axis.

i) What is the intercept of the equal income line?

ii) What is the slope of the equal income line?

b) Graph the equal income line with ln(A), the natural logarithm of cars produced, on the y-axis, and ln(B), the natural logarithm of memos produced, on the x-axis.

i) What is the intercept of the equal income line?

ii) What is the slope of the equal income line?

c) Who will choose to become mechanics? (Hint: The workers on which side of the equal income line?)

d) Who will choose to become stenographers? (Hint: The workers on which side of the equal income line?)

e) Below are four sets of wages.

1. The income from making cars, earned by those who choose to be mechanics

2. The income from writing memos, earned by those who choose to be stenographers

3. The income from making cars earned by those who choose to be stenographers

4. The income from writing memos, earned by those who choose to be mechanics

We can only observe workers income after they have made their career decision.

i) Which wages can we observe?

ii) Which wages can we not observe?

f) True or false? The income of the worst stenographer will be greater than or equal to the income of the best mechanic. Explain your answer.

g) Suppose the government takes the observed incomes of stenographers and uses it to approximate what the incomes of mechanics would be if they switched to become stenographers instead. (So, instead of making cars, they would write memos.) Would the governments approximation correctly represent the income of mechanics if they switched to stenographers If not, would it underestimate or overestimate the actual incomes mechanics would earn if they became stenographers?

h) Suppose the government now takes the observed wages of mechanics and used it to approximate what the wages of stenographers would be if they switched to making cars. Would the governments approximation correctly represent the car-making income of stenographers? If not, would it underestimate or overestimate the true car-making income of those who chose to be stenographers?

From part c on, suppose that everyone's mechanic ability is the same. They would all make 2 cars per hour. Everyone's stenography ability, however, is random. In other words, the number of memos each worker can produce is randomly determined. The graph below represents worker ability. In(A) equal income line x In(2) x X X X In(B) From part c on, suppose that everyone's mechanic ability is the same. They would all make 2 cars per hour. Everyone's stenography ability, however, is random. In other words, the number of memos each worker can produce is randomly determined. The graph below represents worker ability. In(A) equal income line x In(2) x X X X In(B)