Carlos consumes only two goods, apples and bananas. His utility function is U(x, y) = a^3b^2. Before trade, his initial endowment is wa apples and wb bananas. After he trades to his optimal consumption point at these prices, the relative prices change. Carlos is allowed to make further trades if he wishes. a. Carlos will definitely be better off after the price change.
b. Carlos will be better off if the price of the good he was selling goes up and worse off if the price of the good he was selling goes down.
c. Carlos will be better off if the price of the good he was selling goes down and worse off if the price of the good he was selling goes up.
d. Carlos’s utility will not be affected by the change.

Bill is 31 years old, married, and lived with his spouse michelle from january 2018 to september 2018. bill paid all the cost of keeping up his home. he indicated that he is not legally separated and he and michelle agreed they will not a file a joint return. bill has an 8-year-old son, daniel, who qualifies as bill's dependent. bill worked as a clerk and his wages are $20,000 for 2018. his income tax before credits is $500. in 2018, he took a computer class at the local university to improve his job skills. bill has a receipt showing he paid $1,200 for tuition. he paid for all his educational expenses and did not receive any assistance or reimbursement. bill does not have enough deductions to itemize. bill, michelle, and daniel are u.s. citizens with valid social security numbers. 8. bill does not qualify to claim which of the following: a. head of household b. education benefit c. earned income credit d. all of the above