If a firm produces quantities 9 and 92 of two goods, its total cost is: C = 9 +9 +9 aq192. The goods are sold in competitive markets at prices p > 1 and p2. (a) [10 marks] Write down an expression for the profit of the firm. Obtain and provide an economic interpretation for the first-order profit-maximising conditions. (b) [10 marks] Using the Cramer's rule, find the quantities 9 and 92 that satisfy the first order conditions. (c) [10 marks] Find the second-order conditions for profit maximisation. For what values of a are the second-order conditions satisfied? (d) [10 marks] Assume the second-order condition is satisfied. Use calculus to determine the way in which the supply of good 2 varies with a rise in p. Explain why it depends on the sign of a. = = (e) [10 marks] Assume the second-order condition is satisfied. If p 0.5 and p2 1, under which condition about a will good 1 be supplied by the firm? Explain the economic intuition behind the results. If a firm produces quantities 9 and 92 of two goods, its total cost is: C = 9 +9 +9 aq192. The goods are sold in competitive markets at prices p > 1 and p2. (a) [10 marks] Write down an expression for the profit of the firm. Obtain and provide an economic interpretation for the first-order profit-maximising conditions. (b) [10 marks] Using the Cramer's rule, find the quantities 9 and 92 that satisfy the first order conditions. (c) [10 marks] Find the second-order conditions for profit maximisation. For what values of a are the second-order conditions satisfied? (d) [10 marks] Assume the second-order condition is satisfied. Use calculus to determine the way in which the supply of good 2 varies with a rise in p. Explain why it depends on the sign of a. = = (e) [10 marks] Assume the second-order condition is satisfied. If p 0.5 and p2 1, under which condition about a will good 1 be supplied by the firm? Explain the economic intuition behind the results