A household consumes two goods: a consumption good, denoted C, and housing, denoted H. You can think of H as the size of the house the household wishes to rent. The preferences over the two goods are represented by the utility function u (C) + bu (H), where b > 0 is a parameter, and u () is a strictly concave function. The household is endowed with income Y which is completely spent on C and H. The rental price of one unit of housing is p, and the consumption good is the numeraire. This yields the budget constraint C + p