Problem 2 {5" points} Consider a modied version of the Gar}? Becker-style micro model of ferlilitj,F choices. in which both men and women have child-care responsibilities. Suppose that the man in the household has Tm hours of time to devote to market work andfor child care, and that he must contribute on hours per child in care time. His wage in market work is mm. The woman has Tm hours available for market work and}{ or child care; she must contribute Cw hours per child in child care. Her wage is row. The household has no other souroes of income. In addition to parental time, each child requires p in goods such as food and clothing. The household's utilityr function is U = N\" 11'\". with a being a preference parameter such that i] s: a s: 1. [a] Algebraicallv derive and graph the budget constraint and the time constraints for this modied version of the model. Please provide detailed labels in your graph and add explanations. (b) Mat is the desired (utility-maximizing} number of children N" and other consumption it"? {Your solution should be in symbols} Make sure to state clearly.r an};r assumptions that you are making. (c) Show in a carefully labeled graph how the budget oonstraint would change if the man's wage were to increase from w... to mg. ([1] What role does the man's child-care obligation cm play in the position of this new budget constraint (the constraint with the higher wage win) relative to the position of the old constraint l[the one with Him}? In particular, what would happen it' the man's wage rises to win, but cm 2 D, in which case the man would have no child-care time obligation at all. Please explain and show this special case in a graph