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ECON304 Homework #4 ? Desired Capital, User Cost and Goods Market Equilibrium




Question;Name;last 4 PSU ID _______Please;check section that you are registered in:Section 002 -;MWF 8:00 - 8:50 am: 102 Forum;Building ________Section;001 - MWF 1:25 - 2:15 pm: 101 Thomas Building ________Fall 2014 Chuderewicz - YOU MUST HAND IN HW IN THE SECTION YOU ARE;REGISTERED FOR - NO EXCEPTIONS YOU MUST USE THIS AS A TEMPLATE?;THAT IS? MAKE SPACE FOR YOUR ANSWERS BY HITTING ENTER (you certainly don?t;need to type this assignment)? LEAVE THE;QUESTIONS AS THEY ARE? AND PLEASE STAPLE! NOTEBOOKPAPER;(OR ANY PAPER) STAPLED TO THE BACK IS NOT ACCEPTABLE (GETS A ZERO). ALSO, PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME IN THE TOP RIGHT HAND;CORNER OF THIS PAGE SO THAT WE CAN ALPHABETIZE THESE EASILY. THANKS IN;ADVANCE!Economics;304Homework;#4 ? Desired Capital, User Cost and Goods Market EquilibriumDue Wednesday, 10/1 at the beginning of;class ? no late papers accepted!Instructions;Please show all work or points will;be taken off. Good luck! 1. PART 1 (35 points total ?;5 points for each part and 10 points for the diagram) You own a golf course in;Florida and you need to determine how many golf carts you need to buy to;maximize profits. Please answer the following;questions given the information below.A brand new golf cart costs;300 rounds of golf and the rate of depreciation is 15% (.15).The real interest rate is 5%;(use.05 in calculations).The expected marginal product;of capital is given by MPKf =;200 ? 5K.a) What is the user cost of capital and what is;it expressed in??b) How many golf carts should you buy to maximize profits (i.e.;what is K*)?Draw a graph (the uc / MPK;graph) depicting the state of affairs and label this initial profit maximizing;point as point A. A completely labeled and correct graph;is worth 10 points.c) Now suppose the (local) government with all;their financial shortfalls embarks on a campaign to raise revenue to fund the;fire department by imposing a so-called ?luxury tax? (we know it as?) equal to;25% of gross revenue What happens to;the profit maximizing number of golf carts? Please show all work and label as point B on your uc/MPK graph.d) Now explain why your;profit maximizing K* has changed. Please be specific using the firm?s profit maximizing condition (explain the intuition!).;Start your answer with ?If I did not;change my capital input (my K*), then I would not be ??.(you can finish the rest!) ?????..? e) The Federal government;knowing all about the financial pains encountered by state and local;governments given the Great Recession, decide to offer an investment tax credit;equal to 20% (this is in addition to the tax already imposed by the local;government). What is your desired;capital stock (K*) now? (Hint: An investment tax credit effectively reduces the;price of capital to the firm ? think of it as this ? under the investment tax;credit ? you buy a golf cart (cost = 300 rounds of golf) and you get a 20% rebate from Uncle Sam so the investment;tax credit adjusted price of the golf cart is now 240 rounds of golf [(1-.20) x;300 = 240]. Please show all work again;and label this as point C on your uc/MPK diagram.1. PART 2 (NEW GRADER ? 35;points ? 5 for f) and g) 10 for h) and 15 for graph)) Draw a desired investment;diagram (completely labeled with all;the shift variables noted next to the function in parentheses with signs (+ or;-)) depicting the initial;equilibrium as point A (simply draw a negatively sloped ID curve;going through point A). Label the;initial real interest rate as r*A =.05 (as is given above) and the initial;level of desired investment as IdA. Note importantly that;we do not have numbers for desired investment, but that?s ok, we are focusing;on the change in desired investment, given the same real rate =.05. Be sure to;include all ofthe 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 =.05. f) Why did the level of;desired investment change, even though the real rate of interest did not?;Please be specific using the equation that connects the desired capital stock;(K*) to desired investment (as we did in class (equation 4.6?in text). Label this (new) level of;desired investment as IdB (again, we don?t have specific;numbers for IdB.;Be sure to include all ofthe;shift variables in parentheses next to your new ID functionFinally, show how the;investment tax credit maps to your desired investment diagram and label this;final point as point C. Label this (new) level of desired investment as IdC;(again, we don?t have specific numbers for IdC). Make sure you include all of shift variables in parentheses next to your new ID;function.g);Suppose that the Federal Reserve had a goal to get the capital stock (the;number of golf carts purchased) back to its initial level as in part b (this;would create jobs and get the economy back to full employment). Given all the changes (the imposition of the;tax by the local government and the investment tax credit offered by the;Federal Government), what would they have to do to the real rate of interest to;achieve their objective? Please show all;work and I am looking for a specific number (i.e., r =?).h);(10 points) Finally, explain how this most previous development (a change in r);would influence your two diagrams and why.;Show on your two diagrams as point D.;I am asking for a discussion for each diagram (this question is worth;ten points!);2. (45 points total ? 5 points each part;except part e)A closed economy has full employment level of output;(Y) of 2,000. Government purchases, G, are 200, taxes (T) are 400. Desired consumption (Cd) and;investment (Id) are:Cd = 550 +;0.5(Y ?T) - 600rId = 600 -;400ra) 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 points We;now have a change in the desired investment function ? it is now:Id = 570 -;400rc);Name four reasons why the desired investment function would change the way it did.d);Resolve for the goods market clearing interest rate and the associated levels;of desired savings and investment.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 of the 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 4 reasons from c) you are using and clear on why exactly K*;changes using the profit maximizing condition (give me the intuition).f);What has happened to the level of desired consumption and why? Be sure to refer;to the substitution effect in your answer! Be specific with numbers.


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