An economy consists of two individuals, A and B and two goods, a private good, which is called good 1, and a public good, which is called good 2. Each individual i=A,B is endowed with 24 units of time, which can be used to produce an amount x_(1)^(i) of a private good at a labour cost of x_(1)^(i) units of time, and an amount x_(2)^(i) of a public good at a labour cost of 2x_(2)^(i) units of time. Individual i^(2) s utility function is given by u^(i)(x_(1)^(i),x_(2))=(x_(1)^(i))^(1//2)(g)^(1//2), for both i=A,B and where g denotes the aggregate provision of the public good, i.e. g=x_(2)^(A)+x_(2)^(B). (a) Derive the allocation that maximises utilitarian welfare (i.e. the sum of both individual's utility functions). 3