Question 1
Consider a linear model of demand and supply for a certain laptop:
$Q^D = alpha - eta P + gamma G$
$Q^S = heta + lambda P - phi N$
$Q^D = Q^S$
Where the endogenous variables are the price of the laptop (P), the quantity
demanded by consumers ($Q^D$) and the quantity supplied by producers ($Q^S$). The
exogenous variables are the price of goods that are potential substitutes (G) and the
price of inputs used in producing laptops (N). Assume that $alpha, eta, gamma, heta, lambda, phi$ represent the
parameters of the model and that they are all greater than 0.
a) Do not simplify the model and set up the model in matrix form. Call A the 3x3
matrix of coefficients. List the endogenous variables in the following order:
($Q^D$, P, $Q^S$)
[5 marks]
b) Simplify the model and set up the model in matrix form. Call B the 2x2 matrix of
coefficients. List the endogenous variables in the following order: (Q, P)
[5 marks]
c) Compute the determinant of B and explain what the determinant value implies
for our system of equations. What if the determinant was equal to zero?
[5 marks]
d) Find the equilibrium quantity $Q^*$ using Cramer's rule starting from the system of
equations from Question 1b.
