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.

Draw the savings functions for both consumers, side by side on the same diagram and be sure to label which savings function is Dagwoods and which is the Barbers. Show all the calculations. Please completely label each savings function with all the shift variable in parentheses next to each savings function.