ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Please explain to me what every different variable means in this question

1) In period t, a parental household (indexed by i) equipped with human capital h
earns a labour income of whi, where w > 0 represents a constant wage rate. This
household derives utility out of own consumption , the number of children n
and their level of human capital h+1 Education is provided by teachers who are
equipped with the economy's average level of human capital hf. Human capital per
child evolves from one period to another according to
h₁+1 = (e+ē)" (hi)*(h?) ¹—7,
0<n, T <1
(1)
where ē> 0 is a constant parameter and e represents the level of education per
child.
The households' utility function is specified as
U₂ = In(c) + [In(ni) + 3 ln(hi+1)]
with 7,3 > 0.
Raising one child to adulthood requires a share of 0 << 1 units of time. Moreover,
education is subsidised at a rate 0 ≤ se < 1, such that education costs per child
amount to whe(1 - se).
a. Solve household i's optimisation problem and explain the economic rationale of
your results.
b. Let's define a variable a capturing the households' relative human capital en-
dowment with respect to the economy's average, such that
hi
Show that relative human capital of household i, evolves according to
ĐỀ+= = 8)² )" . (²) ²
zat (1-se)ē)
2- - (1 - se)ē
(3)
(4)
c. Suppose the +1-locus (4) intercepts from above at z = 1 with the 45-degree
line. What does this information imply for the evolution of inequality? Explain
the impact of the education subsidy on the +1-locus with an appropriate
diagram.
Remark: No derivations are required here. Just provide a decent rationale
and do as asked!
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Transcribed Image Text:1) In period t, a parental household (indexed by i) equipped with human capital h earns a labour income of whi, where w > 0 represents a constant wage rate. This household derives utility out of own consumption , the number of children n and their level of human capital h+1 Education is provided by teachers who are equipped with the economy's average level of human capital hf. Human capital per child evolves from one period to another according to h₁+1 = (e+ē)" (hi)*(h?) ¹—7, 0<n, T <1 (1) where ē> 0 is a constant parameter and e represents the level of education per child. The households' utility function is specified as U₂ = In(c) + [In(ni) + 3 ln(hi+1)] with 7,3 > 0. Raising one child to adulthood requires a share of 0 << 1 units of time. Moreover, education is subsidised at a rate 0 ≤ se < 1, such that education costs per child amount to whe(1 - se). a. Solve household i's optimisation problem and explain the economic rationale of your results. b. Let's define a variable a capturing the households' relative human capital en- dowment with respect to the economy's average, such that hi Show that relative human capital of household i, evolves according to ĐỀ+= = 8)² )" . (²) ² zat (1-se)ē) 2- - (1 - se)ē (3) (4) c. Suppose the +1-locus (4) intercepts from above at z = 1 with the 45-degree line. What does this information imply for the evolution of inequality? Explain the impact of the education subsidy on the +1-locus with an appropriate diagram. Remark: No derivations are required here. Just provide a decent rationale and do as asked!
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