Answer:
Please find the detailed answer as follows:
Explanation:
Q = KL
Wage = 30
Rent or price per unit of capital = 20
a) A firm minimizes its cost at the point where marginal rate of technical substitution is equal to the ratio of the prices of inputs.
So, marginal rate of technical substitution = marginal product of labor / marginal product of capital = wage / rent
K / L = 30 / 20
K / L = 1.5
K = 1.5L
Q = KL
Putting the value of Q = 600 and K = 1.5L in the above equation,
600 = 1.5L x L
600 = 1.5L2
L2 = 600/1.5 = 400
L = 20 is the answer.
K = 1.5L
K = 1.5 x 20 = 30 is the answer.
So, 20 units of labor and 30 units of capital should be used by firm to minimize the cost of producing 600 units of output.
b)
A firm minimizes its cost at the point where marginal rate of technical substitution is equal to the ratio of the prices of inputs.
So, marginal rate of technical substitution = marginal product of labor / marginal product of capital = wage / rent
K / L = 30 / 20
K / L = 1.5
K = 1.5L
Q = 1.23KL
Putting the value of Q = 600 and K = 1.5L in the above equation,
600 = 1.23 x 1.5L x L
L2 = 600 / (1.23 x 1.5)
L2 = 325.2
L = 18 approximately or rounded off.
K = 1.5L
K = 1.5 x 18 = 27
Total cost = (wage x units of labor used) + (rent x units of capital used)
= (30 x 18) + (20 x 27)
= 540 + 540 = 1080 is the answer.
