Consider the following profit function has been obtained from technology that uses single input.
π(P, W)=P²W² , 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.
a) The value of the bitter parameter that will maximize the profit function of the product and demand for input will depend on the market conditions and the demand for the product. It is not possible to determine the exact value of the bitter parameter without knowing more information about the market.
b) The supply function of the product and demand for input can be calculated by taking the derivative of the profit function with respect to the input price (W):
dπ/dW = 2P²W
Therefore, the supply function of the product and demand for input is 2P²W.