]. Consider a household utility U = in(X), where X is nal goods from home production that directly a'ect the utility. And for X to be produced, Y has to be used. Let th, tw be the time spent by husband and wife in the production of X, And X = Y\" [minm tw})1_ be the production function for nal home production good X. And hh, and h", be the hours they spend in labor market, earning my" and mm. (a) For this family to produce X. From the production function, can you tell the relation- ship between time spent by husband and time spent by wife? (Are they complement, substitutes or neither?) (b) Give some examples of X. ( i.e. What are kind of home production goods can you think of that this production function is mimicking? Try to look at question (a) for hint. ) (e) Please rite down the time constraints for both husband and wife. Given that they all have 1 as total time endowment. (Assuming besides working, they both devote their time into home production.) (d) Given the price of Y is p, And total family non-labor income is V. Please write down the family's budget constraint