Three families grow vegetables in their backyards,and agree to form a small closed economy by sharing their produce. family andrews grow artichokes, family brown grows beans and family Cuthbert grows corn.Family Andrews receives 70% of its artichokes, 30% of the beans and 30% of the corn.Family Brown receives 20% of the artichokes,60% of the beans and 10% of thr corn.Family Cuthbert receives the remainder of the vegetables.
a) Write down the exchange matrix A.
b) If production is measured in doolars ,define the variables
of the production vector X.
c) Find all solution of the Leontief closed with matrix equation (I-A)^-1¤X=0.
d) If family Cuthbert produces $100 worth of corn, how much will familes Andrews and Brown need to produce (in dollars) in order foe the economy to be in equilibrium?