1) In period t, a parental household equipped with human capital ht earns a labour income of wht, where w> 0 represents the constant wage rate. This household derives utility out of own consumption (ct), the number of children nt and their level of human capital ht+1. Education is provided by teachers who are equipped with the economy's average level of human capital ht. Human capital per child evolves from one period to another according to
1) In period t, a parental household equipped with human capital ht earns a labour income of wht, where w> 0 represents the constant wage rate. This household derives utility out of own consumption (ct), the number of children nt and their level of human capital ht+1. Education is provided by teachers who are equipped with the economy's average level of human capital ht. Human capital per child evolves from one period to another according to
Chapter1: Making Economics Decisions
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Problem 1QTC
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a. Solve the household’s optimisation problem with respect to ct, nt , et and explain the economic rationale of your results.
Transcribed Image Text:1) In period t, a parental household equipped with human capital ht earns a labour
income of wht, where w> 0 represents the constant wage rate. This household
derives utility out of own consumption (ct), the number of children nt and their level
of human capital ht+1. Education is provided by teachers who are equipped with
the economy's average level of human capital ht. Human capital per child evolves
from one period to another according to
ht+1 = (et + ē)"ht,
(1)
where ē> 0 is a constant parameter and et represents the level of education per
child.
The households' utility function is specified as
0<n<1
Ut = ln ct + y ln(ntht+1)
with y > 0.
Raising one child to adulthood requires a share of 0 < z < 1 units of time. Moreover,
education is subsidised at a rate 0 ≤ se < 1, such that education costs per child
amount to whtet (1 — Se).
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why is time expense equal to wht(1-z) - what does the income have to do with how much the time cost?
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