Consider the human capital growth model. Let us make the following changes. Depending on whether the current calendar year is an odd or even number, the efficiency parameter of the human capital accumulation technology changes between 5.15 and 2.04. In particular, when the calendar year is an odd number (for example in years 1 and 3) the parameterbis 5.15 andzis 6. However, in even years (for example in years 2 and 4) the parameter is 2.04 and z is 3. Also, let us assume that in each odd yearu= 0.8 and in each even yearu= 0.5. Let the human capital level at the beginning of period 1 beH1= 1. Each consumer has one unit of time which can be allocated between work and accumulating human capital.

1. Calculate the human capital level for years 2, 3, 4, 5, and 6.
2. Calculate the consumption level for years 2, 3, 4, 5, and 6.
3. Prove thatC3/C1=C5/C3andC4/C2=C6/C4.
4. Find the parametersa1, r1, a2, r2such thatCT=a1(r1)^TwhenTis odd, andCT=a2(r2)^T, whenTis even.
5. After how many years will the consumption double?