Assignment on Firm’s Marginal Production

ECON2020C
[DATE]
GRIZLI777

Question 1
Production function
q=5 L K 0.5 +2 L2 K−L3 K
(a) Short run production function for K = 9
q=5 L K 0.5 +2 L2 K−L3 K
q=5 L ( 9 ) 0.5 +2 L2∗9−L3∗9
q=15 L+18 L2 −9 L3
(b) Firm’s marginal production of labour can be indicated by differentiating the output with
regards to labour (L)
q=5 L K 0.5 +2 L2 K−L3 K
dq/dL = 5K0.5 + 4LK -3L2K
Hence, MPL = 5K0.5 + 4LK -3L2K
The above differentiation has been conducted considering that K is constant and only L is the
variable.
Thus, MPL = 5K0.5 + 4LK -3L2K
Average product of labour (APL) = q/L
Thus, based on the given production function, APL = 5K0.5 + 2LK -L2K
(c) Firm elasticity of output with regards to labour = (dq/dL)/(q/L) = MPL/APL
Substituting the values of MPL and APL obtained in part b, we get requisite elasticity =
(5K0.5 + 4LK -3L2K)/ (5K0.5 + 2LK -L2K) = 1+ 2LK(1-L)/(5K0.5 + 2LK -L2K)
Question 2
Production function for Will and David
GW =2.5 A0.36 R0.64
GD=2.5 A0.25 R0.75
1

(a) Marginal productivity of Will and also of David from studying supply and demand
problem
For Will
GW =2.5 A0.36 R0.64
Derivative w.r.t R, MPR of Will=2.5 A0.36∗0.64 ( R )1−0.64=1.6 ( A
R )0.36
For David
Derivative w.r.t R, MPR of David=2.5∗0.75 A0.25 R1−0.75=1.875 ( A
R )
0.25
(b) Marginal rate of technical substitution (MRTS) between studying the two types problem
of Will and also of David
For Will
GW =2.5 A0.36 R0.64
Derivative w. r. t. A, MPA of Will=2.5∗0.36 A1−0.36 ( R ) 0.64=0.9 ( B
A )
0.64
Hence,
MRTS= MPA
MPB =
(0.9 ( B
A )0.64
)
1.6 ( A
R )0.36 = ( 9
16 ) B
A
For David
Derivative w. r. t. A, MPA of David=2.5∗0.25 A1−0.25 R0.75=0.625 ( B
A )
0.75
Hence,
MRTS= MPA
MPB =
0.625 ( B
A )
0.75
1.875 ( A
R )
0.25 =1
3 ( B
A )
2