Suppose that capital markets are imperfect and some workers face borrowing constraints
(cannot obtain loan to finance their education at the market interest rate). What will be the
relationship between marginal benefit and marginal costs of education for these workers?
(a) The marginal benefit of an additional year of schooling will be equal to the marginal cost.
(b) The marginal benefit of an additional year of schooling will be higher than the marginal
(c) The marginal benefit of an additional year of schooling will be lower than the marginal
(d) The marginal benefit of an additional year cannot be compared to the marginal cost.
Suppose that the wage of the worker with the schooling level S and ability A is given
by w(A,S) = A√S. Every period of schooling the worker has to pay tuition F. Government
subsidizes M of her tuition.
1. If ability of worker is A = 2, the market interest rate is r = 0.02 the tuition is F = 8, and
the government pays M = 3 of the tuition, what is the optimal level of schooling for this
2. Suppose the worker is uncertain about the wage she might receive after the graduation.
With the probability 0.4 she expects the wage to be wL(A,S) = 0.5A√S, with probability
0.5 she expects the wage to be wM(A,S) = A√S, and with probability 0.1 she expects the
wage to be wH(A,S) = 3A√S. If the workers is risk-neutral, what is her optimal level of
schooling? (use parameters from 2.1.)
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