Please post work and all formulas. Thank you!

2. Suppose that there are three possible future states of the world, and the utility function is u(x)=logx. Let the probability of state 1,1, be 1/2, and 2=1/3. The prices of the pure securities, p1,p2,p3, equal 0.8,0.6,0.4 in dollar, respectively. An individual has an initial wealth, W0, of 50,000 a. What amouhts will the risk-averse individual invest in pure securities 1,2 , and 3 ? b. How will the individual divide his or her initial endowment between current and future consumption? 2. Suppose that there are three possible future states of the world, and the utility function is u(x)=logx. Let the probability of state 1,1, be 1/2, and 2=1/3. The prices of the pure securities, p1,p2,p3, equal 0.8,0.6,0.4 in dollar, respectively. An individual has an initial wealth, W0, of 50,000 a. What amouhts will the risk-averse individual invest in pure securities 1,2 , and 3 ? b. How will the individual divide his or her initial endowment between current and future consumption