Consider the following version of the two-period consumption model. The consumer's preferences over current and future consumption (c and c) are: U(c,c)=ln(c)+ln(c) Recalling that we denotes lifetime wealth, it can be shown that with these logarithmic preferences, the optimal consumption allocation is c=21we;c=21(1+r)we. The consumer's budget parameters are y=150;t=20,y=144;t=24,r=0.2, where y and y are current and future income, t and t are current and future lump-sum taxes, and r is the real interest rate. (a) Find lifetime wealth. Using the formula for logarithmic preferences, find the optimal levels of current consumption, future consumption and saving. (b) Confirm that the allocation you found is in fact optimal, by checking the tangency condition and budget constraint. (c) Note that if current consumption is c, future consumption must be c=yt+(1+r)(ytc). Confirm that the allocation you found in part (a) is in fact optimal, by completing the following table. Consider the following version of the two-period consumption model. The consumer's preferences over current and future consumption (c and c) are: U(c,c)=ln(c)+ln(c) Recalling that we denotes lifetime wealth, it can be shown that with these logarithmic preferences, the optimal consumption allocation is c=21we;c=21(1+r)we. The consumer's budget parameters are y=150;t=20,y=144;t=24,r=0.2, where y and y are current and future income, t and t are current and future lump-sum taxes, and r is the real interest rate. (a) Find lifetime wealth. Using the formula for logarithmic preferences, find the optimal levels of current consumption, future consumption and saving. (b) Confirm that the allocation you found is in fact optimal, by checking the tangency condition and budget constraint. (c) Note that if current consumption is c, future consumption must be c=yt+(1+r)(ytc). Confirm that the allocation you found in part (a) is in fact optimal, by completing the following table