"1. The total revenue function of a firm producing a differentiated product is given by R = (X,A,Y,B) where X is the firm's output, A is its expenditure on advertising, Y is the total output of all the other firms in the industry, and B is the total expenditure on advertising of all the other firms in the industry. Y and B are given to the firm. For given values of Y and B, the total revenue function is strictly concave in X and. The firm's total cost function is given by:- C = A + C(X) where C(X) is strictly convex. The firm seeks to maximise its profits by choosing appropriate values for its output and its advertising expenditure. a) Write down the firm's profits function and obtain the first-order conditions for maximising profits. Interpret the two first-order conditions. [10 Marks] b) Now totally differentiate the two first-order conditions and show that the equilibrium values of X and A can both be expressed as implicit functions of B and Y. [10 Marks) c) Using the information given in the question along with the following restrictions on the signs of the second-order partial derivatives of the total revenue function: RXA > 0, RAx>0 Rxy 0, RAx>0 Rxy