4. Consider a perfectly competitive firm that can sell any amount of output at the exogenously given market price (Po), but must pay a tax of to for each unit that it sells. its production costs vary with its output level ((1) according to the function: . TC = C0 + HDQZ; a"), C0 > 0, where CD denotes exogenously given fixed costs. The firm chooses its output level to maximize profit. a. Find expressions for the first and second derivatives with respect to the choice variable C1 of the firm's univariate profit function 1t(Q) = (P0 to)Q (C0 + (:02). b. Is the profit function concave at all Q 2 0? Explain. c. Write down the first order necessary condition for a local maximum and solve it for the function that relates the profit-maximizing output level (03\") to its exogenous determinants: P0, to,Co,ao. d. Find an expression that describes the partial derivative dQ*/6t0 and determine its sign. What happens to the profit-maximizing output level if the tax is increased? e. Find an expression that describes the partial derivative 60766}, and determine its sign. What happens to the profit-maximizing output level ifthe firm's fixed costs increase