In a DD model with 3 periods t=0,1,2. Each consumer is endowed with 1 potato at t=0, has probability 1/2 of becoming hungry at t=1 and probability 1/2 of becoming hungry at t=2. Consumer utility is given by u(c)=1-1/c. Storage technology generates a gross return of 1 from period 0 to 1, and return of 1 from period 1 to 2. Investment technology generates a return of 3 from period 0 to period 2. If an investment is liquidated early in period 1, its return is reduced to 0.5.

Suppose all consumers in town pool their potatos together. Of the 100 potatos, they store 50 and invest 50. When t=1 comes, early types are fed with the stored potatoes. When t=2 comes, late types are fed with the invested potatos.

The expected lifetime happiness of a consumer =_____