Answer to Question #212476 in Microeconomics for Clarise

Question #212476

A firm faces the production function below and can buy L at Php240 a unit and K at Php4 a unit.

A. If it has a budget of Php 16,000 what combination of K and L should it use to maximize output?

Q = 2K 0.2 L 0.6


1
Expert's answer
2021-07-01T13:50:06-0400

Q=2K0.2L0.6............(1)Q= 2K^{0.2}L^{0.6} ............ (1)

Wage w = Php 240

rent = Php 4 

Budegt = 16000


Budegt line 

wL+rK=budegtwL+rK = budegt  

Putting values 

240L+4K=16000.......(2)240L+4K = 16000 ....... (2)

Slope of the isocost line =2404= -\frac{240}{4}  

Marginal product of labour MPL=2(0.6)K0.2L0.4MPL = 2(0.6)K^{0.2}L^{-0.4}   

Marginal product of labour MPK=2(0.2)K0.8L0.6MPK = 2(0.2)K^{-0.8}L^{0.6}

Slope of the isoquants =MRTS=MPLMPK=-MRTS =\frac {-MPL}{MPK}


MRTS=2(0.6)K0.2L0.42(0.2)K0.8L0.6=3KLMRTS =\frac {-2(0.6)K^{0.2}L^{-0.4}}{ 2(0.2)K^{-0.8}L^{0.6} }\\=-\frac{3K}{L}


Condition of optimality 

The slope of isoquants = slope of the isocost line 

3KL=24043KL=60K=20L-\frac{3K}{L}=-\frac{240}{4}\\\frac{3K}{L}=60\\K=20L


Putting value of K in isocost equation 

240L+4(20L)=16000240L+4(20L) = 16000

i.e.320L=16000i.e. 320L=16000

i.e.L=50i.e. L =50

So K=20(50)=1000K = 20(50) = 1000

If K = 1000 and L =50, then we get maximum output. 


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment