Given that consumption in the two periods of life are perfect complements, so that c and ci are related as c. = ac. Use the expression for lifetime wealth, as given in equ. (9.12), to show how Williamson's equations (9.15) and (9.16) are derived algebraically. we = y - + + y - to 1 +r. .(9.12) we(1 + r) C = (9.13) 1 t r ta c'= awe(1 + r) (9.14) 1+rta (y - t) (1 + r) + y' -t' C = (9.15) 1 +rta (y - t) (1 + r) + y' -t'] c' = a 1+rta .(9.16)