The television market in South Africa has two major suppliers producing differentiated television models. The monthly demand functions of the two suppliers is as follows:

Samsung: Q1 = 450 - 2(P1) + P2

LG: Q2 = 450 - 2(P2) + P1

The marginal costs of production are R60 per unit and fixed costs are equal to zero.

Suppose the two producers realize that is is in their interest to operate jointly as if they were a monopoly.

a) Write down an expression for the combined profit of Samsung and LG in terms of Q1 and Q2 only

b) Determine the output levels of the two producers at the joint profit maximization equilibrium. Hint take partial derivatives of the profit function with respect to the two quantities and set the expression to zero and solve the resulting simultaneous equations for Q1 and Q2

c) Determine the prices and the profits of the two producers at the joint profit maximizing equilibrium.