Given the Cobb-Douglas production F(K,K) = L^1/4K^1/4, find the derived input demands, the supply function and the indirect profit function. Next, drive the firm’s conditional input demands for labor and capital and the cost function. Using the cost function with output as the decision variable, find the supply function from the profit-max problem. From your conditional demands, determine the derived input demands, explaining how conditional and derived demands are related. Finally, illustrate Hotelling’s Lemma for this technology