(a)Consider a consumer with the utility function (,)=^ab where x is the quantity of good X and y is the quantity of good Y and where a and b are positive constants. Let be the price of good X, be the price of good Y, and M be the consumer's income. What is the optimal level of x and y when the prices of both goods are 10, when M=200 and when a=b=5? X = , y =

(b)Consider a consumer with the utility function (,)=^ab where x is the quantity of good X and y is the quantity of good Y and where a and b are positive constants. Let be the price of good X, be the price of good Y, and M be the consumer's income. What is the optimal level of x and y when =10 and =20 , when M=200 and when a=b=5? X = , y =

(c)Consider a consumer with the utility function (,)=^ab where x is the quantity of good X and y is the quantity of good Y and where a and b are positive constants. Let be the price of good X, be the price of good Y, and M be the consumer's income. What is the consumer's optimal level of utility (or the consumer's indirect utility) when the prices of both goods are 10, when M=200 and when a=b=2?

(d)Consider a consumer with the utility function where x is the quantity of good X and y is the quantity of good Y and where a and b are positive constants. Let be the price of good X, be the price of good Y, and M be the consumer's income. What is the consumer's optimal level of utility (or the consumer's indirect utility) when =10 and =20 , when M=200 and when a=b=2?