Given a cobb – Douglas production function
Q = L0.5 K0.4

And the prices of capital and labour are ksh3 and ksh 4 respectively while the firm outlay is Kshs.108, calculate the optimal combination of factors inputs.

Question

22-11-2021
Business

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Given a cobb – Douglas production function
Q = L0.5 K0.4

And the prices of capital and labour are ksh3 and ksh 4 respectively while the firm outlay is Kshs.108, calculate the optimal combination of factors inputs.

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mdennisjoe28 mdennisjoe28 · Answer 1 · 2021-11-22T21:59:51+01:00

mdennisjoe28 mdennisjoe28

22-11-2021

Answer:

x

Explanation:

because its x

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abiolataiwo2015 abiolataiwo2015 · Answer 2 · 2021-12-02T04:24:02+01:00

Based on the information given the optimal combination of factors input is Ksh 168.

Given:

Q = L0.5 K0.4

Let cost minimization of labor and capital=MRTS =MPl/MPk=w/r

Let Marginal product of labor=dQ/dL = 0.2K

Let Marginal product of capital=dQ/dK = 0.2L

Hence:

Marginal rate of technical

0.2K/0.2L= K/L

Optimal capital of labor ratio

K/L=3/4

Substitute

Q = L0.5 K0.4

108=K3/4 0.5 K0.4

108=0.15K²

Divide both side by 0.15K²

K²=108/0.15

K²=720

K=√720

K=26.83

Substitute

108= L0.5 (26.83)0.4

108=5.37L

Divide both side by 5.37L

L=108/5.37

L=20.11

TC=wL+rK

TC=3(20.11)+4(26.83)

TC=60.33+107.32

TC=167.65

TC=Ksh168 (Approximately)

Inconclusion the optimal combination of factors input is Ksh168.

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Given a cobb – Douglas production function Q = L0.5 K0.4 And the prices of capital and labour are ksh3 and ksh 4 respectively while the firm outlay is Kshs.108, calculate the optimal combination of factors inputs.

Respuesta :

Otras preguntas

Given a cobb – Douglas production function
Q = L0.5 K0.4

And the prices of capital and labour are ksh3 and ksh 4 respectively while the firm outlay is Kshs.108, calculate the optimal combination of factors inputs.