Wednesday
April 1, 2015

Homework Help: math - marginal analyis

Posted by becky on Sunday, August 13, 2006 at 10:31pm.

A factory's output is Q=600K^1/2L^1/3 units, (read 600 x K to the 1/2 power x L to the 1/3 power). K denotes capital investment and L denotes the size of the labor force. Estimate the percentage increase in output that will result in a 2% increase in the size of the labor force if capital investment is not changed.

Q = 600K^1/2L^1/3
Q' = 300K^-1/2L-2/3 (read 300 x K to the negative 1/2 power x L to the negative 2/3 power.)

Percentage Change equation
100[Q'(.02)/Q]
100[300K^-1/2L^2/3(0.02)/600K^1/2L^1/3]=
100[6K^-1/2L^-2/3]/600K^1/2L^1/3=
600K^-1/2L^-2/3/600K^1/2L^1/3

I'm not sure if this is correct so far and where do I go from here?



Your derivative should be with respect to labor force L.

Q = 600(K^1/2)*(L^1/3)
dQ/dL=600(K^1/2)(1/3)(L^-2/3)
200(K^1/2) (L^-2/3)
check that.

Percent change..
dQ=100[Q'(.02)/Q]
100[200*K^1/2)(L^-2/3)dL/600(K^1/2)*(L^1/3)
]
=1/3*1/L*dL]
check that.


And from there..
percent change=1/3*1/L*dL]
= 1/3 (dL/L) where you are given
dL/L=.02

comments? check it all, it is hard to type an error when in ASCII

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

Algebra - Let U = {u, n, i, t, e} A = {n, i, t} B = {n, e} C = {u, n, i, t, e} D...
Chemistry - What is the maximum number of electrons that can occupy a subshell ...
math - The weekly demand for the Pulsar 25 color LED television is represented ...
math - The weekly demand for the Pulsar 25 color LED television is represented ...
Discrete Math - In the questions below determine the size (i.e. cardinality) of...
calculus - the productivity of a country in western Europe is given by the ...
Calculus - The weekly demand for the Pulsar 25-in. color console television is ...
Math - The weekly demand for the Pulsar 25-in. color console television is given...
Microeconomy - uppose the demand for these jets is given by the equation: P = ...
Physics - Compared to yesterday you did 3 times the work in one third the time. ...

Members