4) Consider the labour market signalling model in the lecture where in the labour market, there is a proportion h of high ability workers with marginal product an and 1-h of low ability workers with marginal product a. að < ap. Workers only choose how much education to undertake: high ability type: en, low ability type: e. Each unit of education costs for high ability workers and for low ability workers. c > Ch. Firms decide a wage for each possible education level w(e). In particular, they pay workers their expected marginal product according to their beliefs about their productivity given the education level. Beliefs are determined as follows in equilibrium: • At any education level which is actually chosen, firms correctly anticipate the proportion of each type of worker. For example, o If both types choose the same education level e, = e =e*, the firm believes that a worker with education level e* is high ability with probability h. o If both types choose different education levelse e, the firm believes that a worker with education level en is high ability, while a worker with education level e, is low ability. At any education level which is not chosen, firms can have any beliefs. Consider a potential separating equilibrium where low and high ability workers choose different education levels and respectively. a) What would firms pay for a worker with education level i), ii) e₂? b) Write down the condition which needs to be satisfied if a high ability worker does not want to choose e instead of en c) Write down the condition which needs to be satisfied if a low ability worker does not want to choose e instead of . d) Using b) and c), provide an argument for why , must be more than .
4) Consider the labour market signalling model in the lecture where in the labour market, there is a proportion h of high ability workers with marginal product an and 1-h of low ability workers with marginal product a. að < ap. Workers only choose how much education to undertake: high ability type: en, low ability type: e. Each unit of education costs for high ability workers and for low ability workers. c > Ch. Firms decide a wage for each possible education level w(e). In particular, they pay workers their expected marginal product according to their beliefs about their productivity given the education level. Beliefs are determined as follows in equilibrium: • At any education level which is actually chosen, firms correctly anticipate the proportion of each type of worker. For example, o If both types choose the same education level e, = e =e*, the firm believes that a worker with education level e* is high ability with probability h. o If both types choose different education levelse e, the firm believes that a worker with education level en is high ability, while a worker with education level e, is low ability. At any education level which is not chosen, firms can have any beliefs. Consider a potential separating equilibrium where low and high ability workers choose different education levels and respectively. a) What would firms pay for a worker with education level i), ii) e₂? b) Write down the condition which needs to be satisfied if a high ability worker does not want to choose e instead of en c) Write down the condition which needs to be satisfied if a low ability worker does not want to choose e instead of . d) Using b) and c), provide an argument for why , must be more than .
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:4) Consider the labour market signalling model in the lecture where in the labour market, there is a
proportion h of high ability workers with marginal product and 1-h of low ability workers with
marginal product a₁. a₁ < an.
Workers only choose how much education to undertake: high ability type: e, low ability type: B₁. Each
unit of education costs for high ability workers and for low ability workers. ₂ > C₁-
Firms decide a wage for each possible education level w(e). In particular, they pay workers their
expected marginal product according to their beliefs about their productivity given the education level.
Beliefs are determined as follows in equilibrium:
• At any education level which is actually chosen, firms correctly anticipate the proportion of each
type of worker. For example,
o
If both types choose the same education level = ₁ =e*, the firm believes that a
worker with education level e* is high ability with probability h.
o
If both types choose different education levels en e, the firm believes that a worker
with education level en is high ability, while a worker with education levelet is low
ability.
At any education level which is not chosen, firms can have any beliefs.
Consider a potential separating equilibrium where low and high ability workers choose different
education levelse and respectively.
a) What would firms pay for a worker with education level i) ₁, ii) e₂?
b) Write down the condition which needs to be satisfied if a high ability worker does not want to choose
e instead of e-
c) Write down the condition which needs to be satisfied if a low ability worker does not want to choose
e instead of ₁.
d) Using b) and c), provide an argument for why must be more than 1.
e) For any other education level e ‡ , & (ie off the equilibrium path), write down the lowest and
highest possible wage that firms will pay.
f) Provide an argument for why e = 0 in any separating equilibrium.
Hint: can the low ability worker find a different education level (off the equilibrium path) which gives him
a higher payoff if e > 0?
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