Consider a consumer with the utility function U(x,y)=x^ay^bwhere x is the quantity of good X and y is the quantity of good Y and where a and b are positive constants. Letp_xbe the price of good X,p_y be the price of good Y, and M be the consumer's income.

1)What is the optimal level of x and y when the prices of both goods are 5, when M=100 and when a=b=2?x=? y=?

2)What is the optimal level of x and y whenp_x=5and p_y=10, when M=100 and when a=b=2?

x =?, y=?

3)What is the consumer's optimal level of utility (or the consumer's indirect utility) when the prices of both goods are 5, when M=100 and when a=b=2?

4)What is the consumer's optimal level of utility (or the consumer's indirect utility) whenp_x=5and p_y=10, when M=100 and when a=b=2?