In an economy there are four different groups of people who can spend their money per month between gallons of fuel (Y) or buying clothes (X).

The first group has a utility function U=(X^0.2)(Y^0.3) and a budget of $340,000 per month. The second group has a utility function U=(X^0.5)(Y^0.4) and a budget of $560,000 per month. The third group has a utility function U=(X^0.9)(Y^0.4) and a budget of $4,500,000 per month. And the fourth group has a utility function U=(X^0.3)(Y^0.7) and a budget of $5,200,000 per month.

a) With the above, determine and graph the optimal consumption, the individual demands and the market demand assuming that the prices of clothing are on average $60,000 and that the prices per gallon of fuel are:

P y = {15,000; 37,000; 67,000; 150,000; 500,000}

(Individual demands and market demand can be plotted on the same Cartesian plane)

b) What happens if a natural disaster occurs that requires fuel rationing to 5 gallons of fuel

The fuel is used for transportation, heating and food preparation in each group