VI. Consider the following equation describing the economics of skills formation: #1 = 9(01 1, 1-1) where # is the skills level of child i at age t, If represents investment in i's skills (or education) in period t. Suppose we observe an economy with 9 children, all from families with different income levels (3 low-income families, 3 middle-income families and 3 high-income families). Kids have the same age and study in the same school. However, for the low-income kids we have that g(01, [;) = (0.)* + 1, for the middle income kids g(0;, I;) = (0:)*+ + 17, and for the high income kids we know that g(6;, f;) = (0:)" + 1. 1. Initially assume that If = 0 for all kids and all periods. If Oh = 1 for all kids (i.e. children are born with the same level of skills), compute the skills levels for low-, middle- and high- income kids when t = 3. 2. Compute the average and standard deviation of the individual skill level in this economy in t = 3. E 3. Repeat (2) but now suppose families invest 10% of their income in every period. The income of low-, middle-, and high-income families are respectively: 10, 20, 30. Suppose that there is no government, so families are the only agents allowed to invest in their own kids' skills. 4. Now suppose there is a government which can invest in the skills formation of children (in addition to parental investment), for instance, by hiring better teachers. Consider the following two policies: 6