Question

1. Consider Irving Fisher’s two-period model of consumption. Suppose that the

consumer also pay’s taxes T1 in the present, T2 in future.

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 Y2 to Y’2, as well as real interest rate increases from r1 to r2. 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

Answer 1

a) Irving Fisher deveopedd a model.Rational individuals always prefer to increase the quantity or quality of the goods and services they consume.However ,most people cannot consume as much as they like due to limited income.In other words, people face a buget constraint,which set a limited on how much they can spend.since consumption drcisiode are taken over a period of time.,

Consumers face intertemporal budget constraint,which shows how much income is available for consumption now and future. The constraint reflect a consume today and how much to save for the future.

We can now derive the consumers budget constraints by combining equations (1)and (2)if we substitute the first equation for in to the second equations we get

C2 =(1+r)(Y1-C1)+Y2....(3)

or , (1+r) C1+C2=(1+r)Y1+Y2

b)