Question

In: Economics

duane breeds parrots for a living he has discovred that the production function for parrot q=5kL...

duane breeds parrots for a living he has discovred that the production function for parrot q=5kL
where k is capital and L is labor. the price of l is 20 and for K is 80 what is the optimal mix of labor and capital?

Solutions

Expert Solution

Answer: K: L = 1:4

Solution : Given the production function as:

q = 5 KL. .....(1)

Where K= capital and L = labor

Also, given the price of labor and capital:

PL = w = $20

PK = r = $80

Least cost combination of capital and labor will be :

MPL/ MP​​​​​​K = w/ r. ...... (2)

From equation(1)

MPL= dq/dL= 5K

MPK = dq/dK = 5L

Put the above values in equation(2).

5K/ 5L= 20/80

K/L = 1/4

K:L =1:4 or L =4K

Rahul Sunny answered 2 years ago
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