Question 5 Economic theory suggests that the upper part of the wealth distribution should approximately follow...
Question 5 Economic theory suggests that the upper part of the wealth distribution should approximately follow a Pareto distribution. A Pareto random variable has a density f(x) = 0x-0-1. The parameter 0 governs the speed of the decay of the density function. The larger tthe 0, the faster is the decay and the less unequal the wealth distribution is. The lower the 0, the slower is the decay of the density, and the larger is the share of the wealth in the society that goes to the top-end of the distribution It should come to no surprise to you that the parameter 0 is very im portant in public and labor economics. It is, in fact, deeply related to the optimal value of taxes that we should impose on the economy Suppose that for the population of individuals with wealth above one million dollars, wealth X, measured in millions of dollars, is Pareto dis- tributed with a 0 equal to 1.2.That is, assume that the density of X is given by f(z) 1.2 x x 22, for x 2 1. Compute: a) Pr[X < 2 b) Pr[X> 10 c) E[X d) (Optional) Sketch the graph of the probability density function of X