Let the utility function of the representative consumer be u(c,n)=c^(2/3)(1-n)^(1/3)

Let the production function be y=2k^(1/2)n^(1/2)

c=final good consumption, n=work effort, k=capital services, y=production output.

The household is endowed with k0=1 units of capital.

Write down the household's optimization problem, and then compute the social optimum