Consider a market with four firms. A firm is indexed by j with j = 0, 1, 2, 3. The demand function of each firm is given by:

q0 = 6p0 +0.03p1 +0.03p2 +0.08p3

q1 = 8+0.03p0 p1 +0.04p2 +0.05p3

q2 = 10+0.03p0 +0.04p1 p2 +0.05p3

q3 = 5+0.08p0 +0.03p1 +0.05p2 p3.

Compute equilibrium prices. To do this, write down the first-order condition of all firms and write them in such a way that all prices are on the left hand side and constants are on the right-hand side. Note that this is the same as writing the system in matrix form: A p = b where A is a matrix of 4 4 containing all the coeicients that are multiplied by prices, p is a vector of 4 1 containing all prices, and b is a vector of 4 1 containing all the constants. Assume that ci = 3 for all i. Using these expressions, solve for equilibrium prices. You can do this by hand or using any software you want. A spreadsheet is more than enough as you should note that the solution to the problem is given by p = A1 b so any software that allows you to invert a matrix and multiply (inverted) matrices and vectors is enough. All spreadsheets allow to do this.