Q4 Profit Maximization & Short Run Supply A firm uses a single input x to produce y where y = 4vx. The price of good y is $100 in the market. The input cost $50 per unit. a) What is the firm's profit in terms of x? b) What is x" , the level of the input that maximizes profit? (Hint, set MP, = wx/p) c) Suppose the firm is taxed $25 per unit of its output. Find the new optimal input level. (Hint, assume the price of good y is now = p - t). d) How much revenue does the government raise from the $25 tax? Suppose the government imposed a lump sum tax on the firm equal to the total tax revenue raised from the $25 tax on each unit of output. Find the optimal level of output for the firm. () Which tax leaves the firm with greater profits? Explain