Q1

Q1. (10 marks) A ?rm produces two goods, 1 and 2, and faces the following demand functions gar-(qr), 1' = 1,2, where p, is the price of good 1' and q,- is the quantity demanded of good 1'. Assume p," (q,-) < 0 and p,- " (q,-) = 0. Cost is a function of the product of the outputs of the two goods, that is, C(qlq'z), where C'( Q1Q2) > 0 and C"( qlqg) > 0. Production of good 1 is subsidised by the government with a per-unit subsidy of s. (i) Write an expression for ?rm pro?t. (1 mark) (ii) What are the ?rst order necessary conditions for a maximum? (2 marks) Let the solutions to these ?rst order conditions be (11(3) and (12(3). (iii) Check that you have in fact found a maximum. (2 marks) (iv) Totally differentiate the system of equations found in (ii) above and solve for quds and quds and sign. (6 marks) (v) Provide an economic interpretation of the results found in (iv). (1 mark)