Question

1. Computing growth rates (I): Suppose xt = (1.04)t and yt = (1.02)t. Calculate the growth rate of zt in each of the following cases:
   1. z = xy
   2. z = x/y
   3. z = y/x
   4. z = x1/2y1/2
   5. z = (x/y)2
   6. z = x−1/3y2/3

Answer 1

suppose x grows 4% per time period

and y grows 2% per time period

that is (x^t= 1.04), (y^t= 1.02)

so, after time period

x= 1.04*4%

x= 0.04

y= 1.02*2%

y= 0.02

Accordung to the question ANSWER is

a. z=xy i.e, z= x+y

z= 0.04+0.02

z= 0.06

b. z=x/y i.e, z= x-y

z= 0.04-0.02

z= 0.02

c. z= y/x i.e, z= y-x

z= 0.02-0.04

z= -0.02

d. z= x^1/2y^1/2 i.e, z= x^1/2+y^1/2

z= (0.5*0.04)+(0.5*0.02)

z= 0.02+0.01

z= 0.03

e. z= (x/y)² i.e, z= x²-y²

z= (2*0.04)-(2*0.02)

z= 0.08-0.04

z= 0.04

f. z= x^-1/3y^2/3 i.e, z= x^-1/3+y^2/3

z= (-0.33*0.04)+(0.67*0.02)

z= -0.0132+0.0134

z= -0.0002