Question 1. [Utility Maximization and Choice] Tom's utility on two goods, and , is presented as below. utility = (,)= a) (10 points) If x costs $1 each and y costs $2 each, determine his utility-maximizing consumption quantities for and , assuming he is spending all his money endowment of $10. b) (10 points) Suppose x price drops to $0.5. How much money can Tom save if he adjusts his consumption quantities of and such that he remains at the same level of utility he received in part a)? Question 2. [Utility Maximization and Cross Price Effects] Suppose the utility function for goods and is given by utility = (,)=+ a) (10 points) Calculate the uncompensated (Marshallian) demand functions for and , and explain how (=) or other good's price would affect the demand for and . b) (10 points) Calculate the indirect utility function and the expenditure function for and . c) (10 points) Calculate the compensated (Hicksian) demand functions for and using the expenditure function from b) above and Shephard's lemma, and explain the effects of income or other good's price on the demand for and .