Please solve A-D and show all steps.

1. Consider two identical consumers denoted by 1 and 2, each with income equal to m. Consumers can purchase two goods z and g. The price of each good is normalized to be equal to one. Preferences are given by:

U1 = ln(g1 + g2) + z1

U2 = ln(g2 + g1) + z2

where 0 1.

a) Provide an interpretation of the parameter .

b) Find the Nash Equilibrium for this game, i.e. solve for the equilibrium levels of g1 and g2.

(c) Compute the symmetric allocation that maximizes the following utilitarian welfare function: W = U1 + U2 subject to the aggregate resource constraint (and that treats both players equally).

(d) Under what conditions is the Nash Equilibrium efficient? Explain your answer.