Answer to Question #202641 in Macroeconomics for Tywin

Question

a) Consider a couple whose behaviour follows the unitary household model. Their preferences can be represented by the utility function: U(C^M; C^H) = min (C^M, C^H), where C^M, denotes market goods and C^H denotes home production. Each spouse can work up to 50 hours per week, and those 50 hours can be divided between market work and home production. Joe and Anna are each paid £20 per hour for market work. Joe produces £20 of home production per hour, while Anna produces £30 per hour of home production. How many hours are each of the spouses allocating to home production and market work?

b)  Suppose that Anna is offered a pay raise, so that her hourly market wage increases to £25, and nothing else changes. Will that change the identity of the spouse who works more hours on the market? Explain your answer. [Hint there is no need to calculate the full solution to this case]

Answer 1

(a) According to the above-given information, the utility function is as follows:

U(CM; CH) = min (CM, CH)

The only possible solution which provides maximum benefit would be CM = CH because it is a min function i.e. goods consumed are complements. Any other combination would reduce the level of utility for this couple and therefore, each will allocate 25 hours for CM and CH. 

(b)Moreover, if Anna is offered a pay raise so that her hourly market wage rises to £25, and nothing else changes. It will not change the identity of the spouse who works more hours on the market. This is so because both the individuals are working the same number of hours i.e. 25 and total income in the household is raised followed by the consumption of complementary goods.