We have two consumers, Dagwood and Dagwood's barber who we will refer to from this point on as 'The Barber.' Dagwood and The Barber both prefer to perfectly smooth consumption, consistent with the lifetime theory of consumption. The initial conditions are the same for both consumers and are as follows.

Y (current income) = 300K

a (current wealth) = 0

Yf (expected future income) = 150K

af ( expected future wealth) = 100K

r (the current real rate of interest) = -.05 (negative 5%)

Given that the economy is finally heading toward the port, the Fed decides to raise real rates of interest to .10 (10%). This is the new real rate of interest faced by both consumers, Dagwood and The Barber.

Compare the reaction of Dagwood and The Barber, in terms of the change in their current period consumption, given the rise in the real interest rate, all else constant (this is after The Barber changes his af). Be sure to refer to the substitution and income effects and how they are similar/different for each consumer and explain in detail why they are different.