Midterm 2-Practice Problems 3
I. High School Choice
Degree (HS) or drop out (No).
Two types of individuals, Type 1=rate (r1)
increase, Type 2= (r2); where r1>r2.
Given a base earnings B, PV1 HS=B(1+r1) PV 2 HS=B(1+r2),
cost=C no matter the worker type.
B=100, r1=0.35, r2=0.2, C=22
1.) Optimal schooling choice both types
: PV HS=B(1+r1)-C , PV HS=B(1+r2)-C
PV1 HS=100(1+.35)=135 , PV 2 HS=100(1+.2)=120, PV No=100 [TA did not take Cost
T1=135-22=113, T2=120-22=98, T No=100
[With Cost taken out]
[Earnings do not involve cost in this
PV HS=(1+r) B=B+Br ; PV No HS=B ;
r= PV HS-PV No HS
PV No HS
3.) Gov. gives cash prize P=3, HS incentive to graduate, is this sufficient?
Yes, b/c now if Type 2
receives P=3, cost=(22-3)=19
No School=100; Type 1 always goes to school, Type 2>100 =goes to school
4.) Market perf. comp. & earnings reflect productivity. Social returns= earnings-costs.
desirable from social planner view?
No, in terms of signaling model, education is wasteful &
individuals over-invest in it. Prize artificially increases returns to education and makes
people invest more into a wasteful activity. In HC model, undesirable b/c person makes
optimal choice given costs & returns to education. Prize viewed as a transfer & not real
return to education.
II. On-the-job training
2-period problem, Training takes full period, Untrained=MPL^NT=100 for
all firms if train=MPL
10%; Trained=30%>Untrained; Training costs=10 in 1
period r=.05; Output P=1 both periods; Pay worker W nt=100 both periods. Trained=WT1 in 1st and