using Gadfly
srand(1524)
# number of products
n=5
# nominal prices
p_nom = [1.6
         1.7
         1.5
         0.7
         1.85]
# nominal demand
d_nom = [0.623
         0.811
         0.302
         0.336
         0.110]
# costs
c = [0.9
     1.50
     1.05
     0.1
     0.75]
# A matrix for the true model, which is not the same as yours.
# Your E_hat will not necessarily look like this one.
E =[-1.1   0.18 -0.4  -0.2   0.1
     0.18 -0.9   0.1  -0.3  -0.4
    -0.4   0.1  -0.7  -0.2  -0.3
    -0.2  -0.3  -0.2  -1.0   0.05
     0.1  -0.4  -0.3   0.05  -1.3]
# returns the true demand for a given price
function demand(p_new)
    exp(E*(log(p_new) - log(p_nom)) + log(d_nom) + randn(n)*0.20)
end
# plots a histogram of a list of profits
function plot_profit_hist(profits)
    plot(x=profits, Geom.histogram(bincount=20))
end
# Create the data 
N=75
Prices = zeros(n,N)
Demands = zeros(n,N)
for i=1:N
    Prices[:,i] = p_nom.*exp(0.2*(rand(n)-0.5))
    Demands[:,i] = demand(Prices[:,i])
end