5) [10 points total] In a world with perfect intergenerational income mobility. a parent\" s income has no bearing whatsoever on a child's income. In a world without any intergenerational mobility. a child is destined to end up in the exact same point of the income distribution as the pareirt. In reality, a child's income depends in part of the parent's income. but there is not a perfect 1:1 relationship. In this problem. you will analyze how intergenerational mobility affects the income distribution over time. Dene a parent's percentile rank in the income distribution to be RP. The child's expected rank in the income distribution is RC. Suppose the two are related according to RC = 25 + 0.512.... This implies that a child born to a parent in the middle of the income distribution (i.e.. Rp : 50) is also expected to have income in the RC = 25 + 0.5