Answer the following questions using the production function

Answer the following questions using the production function , where .

Find the rate of technical substitution (RTS) for an isoquant of this production function.Find the RTS in terms of the parameters and variables. Show your work

Solution

q = AK^aL^b

RTS = MPL / MPK

MPL = dq / dL = (A x a x K^aL^b) / L

MPK = dq / dK = (A x a x K^aL^b) / K

So, RTS = MPL / MPK = (a / b) x (K / L)