Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# If the production function is z = 3x2 – 4xy + 3y2 where x is the labour and y is the capital, find the marginal productivities of x and y when x = 1, y = 2. - Business Mathematics and Statistics

Sum

If the production function is z = 3x2 – 4xy + 3y2 where x is the labour and y is the capital, find the marginal productivities of x and y when x = 1, y = 2.

#### Solution

Marginal productivity of labour, (delz)/(delx) = 6x – 4y

Marginal productivity of labour when x = 1, y = 2 is

((delz)/(delx))_{(1,2)} = 6(1) – 4(1)

= 6 – 4

= 2

Marginal productivity of capital, (delz)/(dely) = 0 – 4x(1) + 3(2y)

= -4x + 6y

Marginal productivity of qapital when x = 1, y = 2 is

((delz)/(dely))_{(1,2)} = -4(1) + 6(2)

= -4 + 12

= 8

Concept: Applications of Partial Derivatives
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