Suppose the utility function of the consumer is given byU=AXY= 5X0.3Y0.6such thatX0 andY0. The budget constraint of the consumer is given by 80010X+8Y. All monetary values are measured in dollars.

Treat each of the questions below as distinct questions and provide as much de- tailed asnwer as possible.

(a) What combination ofXandYwill the consumer consume if she wanted tomaximize her utility given the budget constraint?

(b) What combination ofXandYwill the consumer consume if she wanted to maximize her utility given the budget constraint which now gets affected because of a government decision to impose 10% sales tax on all commodities and services?

(c) How will this utility maximizing choice change if the consumer suffers an income loss of $200?

(d) How will this utility maximizing choice change the if consumer now receives a federal stimulus payment of $500 after having suffered an income loss of $100?