Hi, can you help me with this question?

Consider the following production function for a firm that is a price taker in both input and output markets and uses labour L priced at w and capital K priced at v as the variable inputs to produce output Q which it sells at price p: Q = L1/4 K1/4 a) Set up the firm's long run profit maximisation problem (with both capital and labour as variable inputs) and solve to find an expression for supply (Q in terms of p, v, w) and for the firm's profit (it in terms of p, v, w). [Hint: break this down into steps: expansion path; optimal input demands; total cost function etc.] (15 marks b) Given that the firm is perfectly competitive and hence a price-taker, find an expression for the firm's marginal cost and explain how this relates to the firm's supply curve in the long run. (5 marks) c) If we were to compare a firm's costs to produce a given level of output in the shor run and the long run, which would we typically expect to be higher and why