Suppose we have Dagwood, who has a current income of $200K and expected future income of $160K. He has zero in current wealth and zero expected future wealth. Dagwood's behavior is consistent with the life-cycle theory of consumption. For one, he perfectly smoothes consumption and two, since he is in his peak earning years, he is saving now so that he can maintain his current level of consumption in the future. Given that Dagwood faces a real interest rate of negative 5% (- 0. 05). Please answer the following questions.

a) Calculate Dagwood's optimal consumption bundle showing all work. Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal consumption bundle as point C*_A(be sure to label the no lending / no borrowing point(s) = NL/NB and the slope of the budget constraint(s))

b) Now Dagwood goes to the doctor and finds out that he is not as healthy as he thought (too many eating binges!). The doctor tells him that he is fine now but next period he is likely to be ill and that if you had anything in life that you really wanted to do (as in leisure), you should do it now. As a result, Dagwood's preferences change so that he prefers to consume like our friend Homer, that is, Dagwood prefers to consume twice as much today relative to next period. Resolve for Dagwood's optimal consumption bundle, given these new preferences, and label as point C*_B

c) Ben Bernanke and the Fed are finally happy with the way the economy is headed and to be honest, is now fearful of overheating. As such, the Fed tightens and the real rate of interest rises to 10% (0.10). Given his change in preferences as above in part b), recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*_C.

d) Is Dagwood better off or worse off due to the rise in the real rate of interest? Be sure to define the income effect and the implications of the income effect on Dagwood's current consumption. Then define the substitution effect and the implications of the substitution effect on Dagwood's current consumption. Comment on whether these income and substitution effects work in the same or opposite direction (i.e., is it a tug of war or do they work in the same direction?) in this particular case?

e) How would your answer to d) above change if Dagwood never went to the doctor and maintained his original perfect smoothing preferences. Be specific and again, refer to the income and substitution effects and whether or not they work in the same or opposite directions and why (for full credit).

You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits. Please answer the following questions given the information below. Please be sure to SHOW all work! A brand new fishing pole costs 400 fishing hours (this is your output) and the rate of depreciation is 10% (0.10). The real interest rate is 2% (.02). And the expected marginal product of capital is given by MPK^f = 300 - 5K. The firm also faces an effective tax rate on capital, what we call tao () = 20% (.20) a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in? (Show work)

b) How many fishing poles should you buy to maximize profits? Show work (5 points) Draw a uc/K graph depicting the state of affairs and label this initial profit maximizing condition as point A.

c) Now conditions change as the value of the US dollar appreciates and since you purchase your fishing poles from abroad, the real price of brand new fishing poles falls to 300 hours of fishing Resolve for K* and show as point B on your uc/K diagram.

d) Explain the intuition underlying the change in the profit maximizing level of fishing poles (i.e., why does the firm change its behavior?), making sure you refer to the firm's profit maximizing condition (write it out!). Be specific and write like you were a professional economist! (use some jargon!).

Now suppose we experience two more changes simultaneously (in addition to the change in the real price fishing poles above). In particular, you change your expectations on the marginal productivity of capital, since you feel that the economy is finally recovering from a long drawn out recession (positive animal spirits) and as a result, your new expected marginal product of capital function is: MPK^f = 400 - 5K. The Fed feels the same and raises the real rate up to 0.10 (10%) to keep the economy from 'overheating.'

e) Resolve for the profit maximizing level of fishing poles given these two (simultaneous) additional changes and add this point to your diagram as point C.(show work)

f) Finally, draw a desired investment diagram (completely labeled with the relevant shift variables noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped I^Dcurve going through point A). Label the initial level of desired investment as I^d_A. Note importantly that we do not have numbers for desired investment, but that's ok, we are focusing on the change in desired investment. Then show, as point B, the new level of desired investment as I^d_B. Finally, show how the contractionary Fed policy along with the change in the MPK^f maps to your investment diagram and label as point C with the corresponding level of investment labeled as I^d_C. (make sure you include the relevant shift variables in parentheses or points will be taken off).

Open Economy - Two Large country problem

USA Initial Conditions

Cd = 310 + 0.4(Y-T) - 200rw

Id = 120 - 200rw

Y = 1000

T = 200

G =275

China Initial Conditions

CdF = 480 + .4(YF - TF) - 300rw

IdF = 255 - 300rw

YF = 1500

TF = 300

GF = 300

a) What is the equilibrium real interest rate that clears the international goods market? Show all work.

b) Compare the level of absorption in each country to the income generated in each country. Is the US spending beyond its means? Is China the lender? Explain using real numbers!Draw two diagrams side by side, with the USA on the left and China country on right. Locate this initial equilibrium as points A on both diagrams (there are four point A's, two on each diagram). Be sure to label diagrams completely labeling the trade deficit/surplus on each graph, etc.

c) Now let the US conduct expansionary fiscal policy so that G rises by 300 to 575. We assume that the government spending multiplier (Y/G) is 1.5, consistent with the multiplier estimated by the White House economists. Re-calculate the new equilibrium real interest rate that clears the international goods market and the associated new levels of desired savings and investment for each country and label these new equilibrium points on your existing diagram as point B. Please show all work.

e) Are these results consistent with the US going to AA, the proposition put forth by Fareed-Zakaria in the Colbert clip? Why or why not?

f) Explain what would happen to the trade balance for the US if China experiences a recession (i.e., China's output falls), all else constant. Please be specific as to what would happen to US absorption and why. Feel free to support your answer with a diagram or two.