Consider Irving Fisher's two-period model of consumption. Suppose that the consumer also pay's taxes T 1 in the present, T 2 in future. (Make sure your answers are in order to get full credit)

a. Derive the inter-temporal budget constraint of the consumer.

b. Draw a graph that would represent optimization of consumption. Label the graph clearly.

c. Suppose future taxes decrease to T' 2 . Using a graph, show the effect of this on optimal consumption. Show in a new graph

d. Suppose the consumer's future income increases to Y 2 to Y' 2 , as well as real interest rate increases from r 1 to r 2 . Show the effect of this on the consumer's optimal choice of present and future consumption. Would your result depend on income and substitution effect?

Demonstrate the effect for:

i. When the consumer is a borrower. Show in a new graph

ii. When the consumer is a lender. Show in a new graph