This exercise is about private consumption. Consider a household that lives for two periods. In period, the real labor income is given by Yjl for

={1,2}. There is zero initial real wealth. The real interest rate is. The household has a constant relative risk aversion (CRRA) utility function. The lifetime utility function reads U(C1,C2)=u(C1)+u(C2)=1C111+1C211

where>1, and(0,1)is the subjective discount factor of the household. is consumption in period for={1,2} The lifetime budget constraint is

C1+1+rC2=Y1l+1+rY2l

Given this setup, the household maximises lifetime utility subject to the lifetime budget constraint. We know that this gives the optimal condition:

u(C2)u(C1)=1+r

What is the utility-maximising level of consumption for period 1? (Hint: the final expressions for consumption in both periods should not feature either C1or2

Select one or more:

a. C1=((1+r))1+(1+r)1[Y1l+1+rY2l]

b. C1=((1+r))1(1+r)1[Y1l+1+rY2l]

c. C1=((1+r))1+(1+r)1[(1+r)Y1l+Y2l]

d. C1=((1+r))1(1+r)1[(1+r)Y1l+Y2l]