Assume Elinor works in period 1 and earns an income of 100. She is retired in period 2 and lives off her savings. She can save this period 1 income or spend it on consumption. Whatever she saves in period 1 doubles in value by period 2, and she can spend this money on consumption in period 2. Assume the return on her savings is risk-free, that she spends all her money over the course of her life, and that she lives 2 periods.
a. How much will Elinor have to live on in period two if she spends NOTHING in period one?
b. Call her consumption spending in period 1 ‘N’ (for ‘Now’). Write down an equation relating her savings in period 1, ‘S’, to her income (100) and N.
c. Call Elinor’s second period consumption ‘L’ (for ‘Later’). Write down a relationship between S and L.
d. Use your results from sections a-c to write down Elinor’s 2 period budget constraint. Sketch this constraint. Put L on the vertical axis and N on the horizontal axis.
e. Assume Elinor has preferences described by the utility function U(N,L) = NL2. Find her optimal choice for N and L.