Consider the following profit function has been obtained from technology that uses single input.

π(P, W)=P²W^B , were P is the output price and W is input price and B is bitter parameter value.
a) For which value of bitter parameter the profit function of the product and demand for inout.
b) Calculate the supply function of the product and demand for input.

1 answer

a) The value of the bitter parameter that will maximize the profit function of the product and demand for input is B = 1.

b) The supply function of the product and demand for input is P = W^(1/B). In this case, the supply function is P = W^(1/1) = W.