Question
A company produces two goods, labelled as A and B. Its total costs are: TC= 5QA + 20QB + QAQB Where QA represents the quantity
A company produces two goods, labelled as A and B.
Its total costs are: TC= 5QA + 20QB + QAQB
Where QA represents the quantity produced of good A and QB the quantity produced of good B. The inverse demand functions for good A and B are, respectively:
PA= 40 - QA
PB= 40 - 1/3 QB
Where PA and PB represent the price of good A and B, respectively.
(a) Use partial differentiation to find the output quantities of good A and B that maximise the firm's profit. [6 marks]
(b) Find the prices the firm should charge. [1 mark]
(c) Find the maximum profit. [1 mark]
(d) Use second order conditions to check that your answer to part (a) is a maximum. [3 marks]
(e) Find marginal revenue and marginal cost for each good. Are the two goods complements, substitutes or independent in production? How about in consumption? Briefly explain.
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