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Penn ECONOMICS 304 – Homework 4 – Desired Capital, User Cost

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Penn ECONOMICS 304 – Homework 4 – Desired Capital, User Cost

Homework #4 – Desired Capital, User Cost and Goods Market EquilibriumDue Friday, 9/30 at the beginning of class – no late papers accepted!Instructions: Please show all work or points will be taken off. Good luck!1. (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishingpoles you need to buy to maximize profits. Please answer the following questions given the informationbelow. Please be sure to SHOW all work!A brand new fishing pole cost 1600 fishing hours (this is youroutput) and the rate of depreciation is 7%.The real interest rate is 3%.And the expected marginal product of capital is given by:MPKf = 300 – 5K.There is a tax on capital so tao (?) = 20% (.20)a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in? (Show work) (5points)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 pointA.A correctly drawn and completely labeled diagram is worth 15 pointsc) Suppose that your expected marginal product of capital to change to: MPKf = 310 – 5K. What wouldcause such a change in the expected marginal capital? I am looking for two reasons.1d) Resolve for K* and show as point B on your uc/K diagram ( 5 points).e) Explain the intuition as to why you changed your behavior, why the profit maximizing level of fishingpoles has changed. Be specific and write this like you were a professional economist! Be sure to comparethe actual user cost to the actual MPKf before and after the shock to MPKf, holding K constant at itslevel from part c). (10 points).f) Now conditions change again. Since you buy the fishing poles from Japan and given that the Bank ofJapan (BOJ) has nominal interest rates in negative territory, the US $ appreciates so that the nominal andreal price of fishing poles falls to 1560 fishing hours. (the shock to MPK above still applies – this is inaddition to the shock to MPK).g) Resolve for K* and show as point C on your uc/K diagram ( 5 points).h) Explain the intuition as to why you changed your behavior, why the profit maximizing level of fishingpoles has changed. Be specific and write this like you were a professional economist! Be sure to comparethe actual user cost to the actual MPKf before and after the shock to MPKf, holding K constant at itslevel from part c). (10 points).1. PART 2 (NEW GRADER – 40 points – 5 for h) and 10 for i) and j) and 15 for graph)) Draw a desiredinvestment diagram (completely labeled with all the shift variables noted next to the function inparentheses with signs (+ or -)) depicting the initial equilibrium as point A (simply draw a negativelysloped ID curve going through point A). Label the initial real interest rate as r*A = .03 (as is given above)and the initial level of desired investment as IdA. Note importantly that we do not have numbers for desiredinvestment, but that’s ok, we are focusing on the change in desired investment, given the same real rate = .03. Be sure to include all of the shift variables in parentheses next to this initial ID function.A completely labeled and correct graph is worth 15 points.Then show, as point B, the new level of desired investment, at the same real rate = .03.h) Why did the level of desired investment change, even though the real rate of interest did not? Please bespecific using the equation that connects the desired capital stock (K*) to desired investment (as wedid in class).i) (10 points) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishingpoles purchased) back to its initial level as in part b. Given the two shocks as above, what would they haveto do to the real rate of interest to achieve their objective? Please show all work and I am looking for aspecific number (i.e., r = ?).j) (10 points) Finally, explain how this most previous development (a change in r) would influence yourtwo diagrams and why. Please add this development to BOTH OF YOUR DIAGRAMS (the UC/Kdiagram and the desired investment diagram) as point D. I am asking for a discussion (this question isworth ten points!)2. (45 points total – 5 points each part except part e) and 15 points for Sd : Id graph. A closedeconomy has full employment level of output (Y) of 2,500. Government purchases, G, are 300, taxes (T)are 500. Desired consumption (Cd) and investment (Id) are:Cd = 600 + 0.5(Y –T) – 700rId = 650 – 300r2a) Solve for the desired savings function in intercept – slope form (note, the intercept is an integer).b) Now solve for the goods market clearing interest rate. Please show all work.Draw a desired savings/investment diagram locating this initial equilibrium and point A.A correct and completely labeled diagram is worth 10 pointsWe now have two shocks that occur simultaneously:i) a change in the desired investment function – it is now:Id = 660 – 300rii) a change in taxes = T, the Gov. lowers them to 450c) Name five reasons why the desired investment function would change the way did.d) Resolve for the goods market clearing interest rate and the associated levels of desired savings andinvestment.Add this development to your diagram and label as point B.e) (10 points – discussion = 5 and correct and completely labeled diagram = 5) Choose one and only one ofthe reasons from part c and show the movement from point A to point B using a user cost – MPKf diagram.Please be clear on which of the 5 reasons from c) you are using. Explain the intuition in the movement frompoint A to point B.



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