Question

Find the rate of change of output with respect to time, if production function is Q=A(t)KᵃLᵃ, where A(t) is and increasing function of t. and K=K₀+at, and L=L₀+bt.

Answer 1

The rate of change of output with respect to time in the given production function can be found using the derivative of the function.

Step-by-step explanation:

The rate of change of output with respect to time can be found by taking the derivative of the production function Q with respect to time t. In this case, Q = A(t)K^aL^a.

Using the chain rule, we can differentiate each term separately. The derivative of A(t) with respect to t is A'(t) and the derivative of K with respect to t is a. Since L does not depend on time, its derivative is 0.

The rate of change of output with respect to time is therefore:

dQ/dt = A'(t)K^aL^a + aA(t)K^(a-1)L^a