4. Public goods: Suppose that there are two roommates sharing a kitchen, where both get benefits from having a clean kitchen. Roommate X gets MBX= 35 0.5D in marginal benefits from D dishes cleaned. Meanwhile roommate Y gets MBY= 35 0.25D. They both have increasing marginal costs of doing dishes represented by MC = 3D. (a) (2 points) How many hours of dishes will roommate X do if they are only considering their own private benefits. (b) (2 points) What is the socially optimal allocation (hours of dishes done) when considering both roommates private benefits? (c) (2 points) Intuitively explain why your answer from part A is different (or the same as) your answer from part B. (d) (4 points) Draw a labelled diagram with the private marginal benefits curves, social marginal benefit curve, marginal cost curve. Label the quantity of dishes done when each roommate only considers their own private costs and the efficient amount of hours of dishes