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 consumersand are as follows.

Y (current income) = 300K

a (current wealth) = 0

Y^f(expected future income) =150K

a^f( expected future wealth) = 100K

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

a)(5 points) Calculate Dagwood and The Barber'soptimal consumption bundle showing all work.Since conditions are exactly the same for both consumers

Now draw two completely labeleddiagrams (the two period consumption model) depicting these initial optimal consumption bundles as points C*_A. Please put the diagrams next to each other with the left diagram representing Dagwood and the right diagram representing The Barber. Note that C*_Ais exactly the same for both consumers.

20 points for each correct and completely labeled diagram

As you can tell from the comic above, The Barber is very optimistic about his 401K plan which is his retirement money - representing expected wealth = a^f. As such, The Barber's expected wealth has gone up to 200K (from 100K). Dagwood, on the other hand, is not so excited about the future since his retirement money is in bonds, not stocks, so his expectation of future wealth does not change.

b) (5 points) Calculate The Barber's new optimal consumption bundle showing all work and label as pointC*_Bon the diagram representing The Barber.

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.

c)(5 points) Calculate Dagwood's new optimal consumption bundle depicting his new optimal consumption bundle as point C*_B.

d)(5 points) Calculate The Barber's new optimal consumption bundle depicting his new optimal consumption bundle as point C*_C.

e) (20 points) 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 a^f).Be sure to refer to the substitution and income effects and how they are similar/differentfor each consumer and explain in detail why they are different. Please be very specific and use real numbers! Do the substitution effects and income effect work in the same or different direction for each consumer?

f) In the space below, 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. For the Barber, this savings function is after his change in expected wealth.