Suppose the utility function of the consumer is given by U = AXY = 5X0.4Y 0.5 such that X 0 and Y 0. The budget constraint of the consumer is given by 500 8X +10Y. 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 of X and Y will the consumer consume if she wanted to maximize her utility given the budget constraint?

(b) What combination of X and Y will 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 $100?

(d) How will this utility maximizing choice change the if consumer now receives a federal stimulus payment of $200 after having suffered an income loss of $100?

(e) How will this utility maximizing choice change the if consumer now faces an interna- tional trade war that leads to a 20% increase in the price in commodity X but no change in the price of commodity Y ?