Consider the following simple economy which consists of two industries, guns (1) and butter (2) and is characterized by the following input-output matrix.
Suppose also that the input-output vector of labor inputs is a=[.2 .4]. Suppose consumers are expected to demand 10 units of guns and 20 units of butter. Also assume that the numeraire wage rate is w0=10.
a. Find the equilibrium quantities of guns and butter necessary to satisfy consumer demand.
b. Find the equilibrium prices to charge for each good.
c. Verify that the economy is in equilibrium.
d. How many workers are employed?
e. Show that profits are zero in all industries.
f. Are the Hawkins-Simon conditions satisfied? What would happen if they were not satisfied?
g. What would happen if the wage rate doubled?