Q. Find true or false or uncertain and explain why?

1. [T,F,U] Suppose that at an initial cost of $1000, a homeowner can insulate his house and save $50 each year in heating bills. If the interest rates are 6%, should the house owner insulate or not?

2. [T,F,U] Tweedledee and Tweedledum are similar in every way except that Tweedledee has preferences over tea (T) and biscuits (B) given by U1(T,B) = log(T) + log(B) while Tweedledum has preferences given by U2(T,B) = 2TB. Though we can't observe the utility they derive, we can tell them apart from their behavior because Tweedledum will drink more tea than will Tweedledee.

3. [T,F,U] A consumer has preferences U(x1; x2) = α log(x1 + ?) + (1- α) log(x2), where x1 is food, and x2 is other goods. If Engel's Law holds for this consumer, what can we say about the value of the preference parameter ??