Jeff considers one banana to be equivalent to three apples. a. Let a denote apples and b denote bananas. Write down a utility function U(a, b) that represents Jeff’s preferences over apples and bananas. b. Jeff has an income of Y and the prices of apples and bananas are pa and pb, respectively. Derive Jeff’s ordinary Marshallian demand functions for apples and bananas. Do these demand functions satisfy the law of demand? c. Derive Jeff’s Hicksian demand functions for apples and bananas. 4. Claudia has the following preferences over two goods, c and d:

Interview notes mike is 50 and made $36,000 in wages in 2017. he is single and pays all the cost of keeping up his home. mike's daughter, brittany, lived with mike all year. brittany's son, hayden, was born in november 2017. hayden lived in mike's home since birth. brittany is 25, single, and had $1,500 in wages in 2017. she is not disabled. mike provides more than half of the support for both brittany and hayden. mike, brittany, and hayden are all u. s. citizens with valid social security numbers. 4. who can mike claim as a qualifying child(ren) for the earned income credit?