For the production function P = 3(L)^0.4 (K)^0.6, find the marginal productivities of labour (L) and capital (K) when L = 10 and K = 6. [use; (0.6)^0.6 = 0.736, (1.67)^0.4  = 1.2267]

The demand for a commodity A is q = 80 - \({ p }_{ 1 }^{ 2}\) + 5p₂ - p₁p₂. Find the partial elasticities \(\frac { { E }q }{ { E }p_{ 1 } } \) and \(\frac { { E }q }{ { E }p_{ 2 } } \) when p₁ = 2, p₂ = 1.

The total cost function y for x units is given by y = 4x\(\left( \frac { x+2 }{ x+1 } \right) +6\), Prove that marginal cost decreases as x increases.

A certain manufacturing concern has total cost function C = 15 + 9x - 6x² + x³ . find Find x, when the total cost is minimum 

Verify Euler’s theorem for the function \(u=\frac{1}{\sqrt{x^2+y^2}}\)