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5. (15 pts) The graph below shows households' choice between housing quality (Q) and other consumption (C). The downward-sloping line is the budget constraint. There are two types of households, those with a high preference for housing whose indifference curve is repre- sented by y", and those with a low preference whose indifference curve is represented by #2 With the original budget constraint, the optimal choices of consumption bundles are in point a and point b, respectively. C Now in order to improving people's living condition, suppose the government provide pub- lic housing for free. To keep the cost low, the free public housing is nothing luxurious, it has a quality ti. Suppose t? is higher than point b but lower than point a. In other words, the quality of public housing is higher than the optimal housing choice for L-type households, but lower than that for H-type households. Both H- and L-type households are eligible for the free public housing program. (a) (5 pts) In your answer sheet, show the new budget constraint (you need to reproduce the graph above in your answer sheet, then illustrate the new budget constraint). Show the L-type households under the new budget constraint. Will the L-type household choose to live in the free public housing? (b) (10 pts) Show two scenarios for the H-type household's choice under the new budget constraint. In the rst scenario, the H-type household's optimal choice is to not take 3 the free public housing and its optimal consumption bundle is unchanged at b. In the second scenario, the H -type household's optimal choice involves taking the free public housing. Since the quality of public housing is lower than H-type household's optimal housing choice under the original budget constraint, in the second scenario, the H -type household actually chooses a worse housing quality due to the government program that aims at improving living condition. This phenomenon is called "opt into welfare."