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Preliminary Examination Dev elopmen t Economics F all 1997
Dev elopmen t Economics
Preliminary Examination
F all 1997
Instructions : Answ er THREE 3 of the follo wing FIVE 5 questions. Mak e whatev er
assumptions are necessary .
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Preliminary Examination Dev elopmen t Economics F all 1997
Question 1
Assume that the pro duction function for a represen tativ e rm i is giv en b y
1


Y = AK
 KL  ;
i
i
i
where 0 < < 1, Y is output of rm i , K is the capital sto c k used b y rm i , L is
i i i
the lab or used b y rm i , and K is the aggregate capital sto c k whic h is tak en as giv en b y
rms when maximizing prots. Assume that consumers c ho ose a consumption path c  t 
that maximizes their utilit y function
Z
1

1
c  t 
1

t
e
dt
1

0
sub ject to the budget constrain ts
c +_ a = ra + w;
where a are the p er-capita asset holdings, r is the in terest rate, and w is the w age rate.
Assume that all p eople w ork and that the p opulation L is constan t. Finally , assume that
the depreciation rate for capital is  .
a The gro wth rates for the aggregates c = C=L , k = K=L , and y = Y=L are equal to
the same constan t, g . Deriv e the form ula for g and in terpret y our result.
b Compare the gro wth rate of the decen tralized econom y to that of the so cial planner
who c ho oses consumption