QUESTION A1 (compulsory) Discuss how an economist could use calculus, to advise a firm on how to maximise profits. In particular, consider the case where a firm has estimated an equation in which their Total Cost of production is a function of quantity they produce; and estimated the equation of the demand curve, in which price is dependent on the quantity they sell (assuming they sell all the goods they make). Explain how this information can be combined into a single equation for the firm's total profit (dependent on quantity); and how calculus can then be used to find the profit-maximising level of output. Include, in your answer, whether this optimisation problem requires differentiation or integration. Also discuss how the 'second-order condition' can be used to check the output level gives the maximum profit, rather than a minimum profit.