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  Tutorial-4 Engineering Economics and d capital, the marginal productivity of  Q. 1 If, for a partic particula ularr combin combinati ation on of labour an capital is 6 units of output and the marginal rate of technical substitution is 2 units of capital  per unit of labour, calculate the marginal marginal productivity of labour. labour.

MRTS LK =MP =MPL/MPK  MPK = 6 2 unit=MPL/6 units So MPL=12 units

Q.2 Let the price of capital be Rs. 60 and that of labour labour Rs.0. !rite !rite the Iso"cost e#uation for the outlay of Rs.2000.

2000= 60L+50K  Labour Units=L Capital Units=K 

Q.$. %or each of the follo&ing functions determine &hether return to scale are decreasing or  increasing or constant' (a) Q*+L (b) Q*100-$+-2L (c) Q* aL b &here a*0.6, b*./ (d) Q* aL b &here a*0., b*.0 (e) Q*2-$L-+L

a) Decr Decreas easin ing g retur return n Q=1/1= 1 Q= 2/2= 1 b) Q*100-$+-2L When K = 1 and L = 1 Q=100+3+2=105 When K = 2and L = 2 Q=100+6+4=110  There!re  There!re this this "r!ducti!n "r!ducti!n uncti!n uncti!n "#an describes describes decreasing decreasing return returns s t! sca#e the !ut"ut increase b$ #ess than the "r!"!rti!n b$ %hich the in"uts are increased&

c) Q* aL b &here a*0.6, b*./  onstant R3 a-b*1 d) he production function Q * 20 + 0.6 L 0.0 signifies

' = 0&6(  = 0&5( ' +  = 0&6 + 0&5 = 1&1&  There!re( this "r!ducti!n uncti!n describes di*inishing returns t! sca#e since ' +   1& e) he production function Q * 2+ - $ L - +L signifies When K = 1 and L = 1 Q=2+3+1=6 When K = 2 and L = 2 Q = ,2 - 2) + ,3 - 2) + ,2 - 2) = 4 + 6 + 4 = 14  That is %hen in"uts are d!ub#ed the !ut"ut *!re than d!ub#e& .ence the "r!ducti!n uncti!n describes increasing returns t! sca#e&

Q./ ien the !##!%ing "r!ducti!n uncti!n and in"ut "rices( esti*ate the

!"ti*u* in"ut c!*binati!ns ! L  K( assu*ing that r* has !n#$ s& 6000 t! s"end& dditi!na##$ assu*e "r!t *a-i*iati!n as the !bectie uncti!n ! the r*7 Q= LK890L :L=60( :K=30 Where Q the #ee# ! !ut"ut "r!duced( L is #ab!ur units ; K is the units !  ca"ita# used (:L =%age rate and :K the rate ! interest MRTS=MP L/w=MPK /r MPL/MPK =K-0L Pl/P! =60/"0 2L=K-0 L=K/2-#0 60L+"0K=6000$$$$$$$ %so &ost '(uation 60 )K/2-#0*+"0K =6000 "0K-2#00+"0K= 6000 60K= 6000+2#00 60K= #00 K=#00/60 K=1#0 Substitutin K in %so-&ost '(uation 60L+1#0,"0=6000 60L=6000-#200 L=100/60 L="0