QUESTION A1 (compulsory) Discuss how an economist could use calculus, to advise a firm on how to maximise profits. In pa

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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. Type your answer into the
box. The word length should be about 500 words (plus or minus
10%).