Name Date last 4 PSU ID Economics 304WD Homework Lesson 5 The Desired Capital stock Investment Demand and Goods Market Equilibrium 120 Points 5 points each part 1 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 2000 rounds of golf and the rate of depreciation is 5 The real interest rate is 8 The expected marginal product of capital is given by MPKf 1000 10K a What is the user cost of capital and what is it expressed in uc b How many golf carts should you buy to maximize profits i e what is K K c Draw a graph the uc MPK graph depicting the state of affairs and label this initial profit maximizing point as point A 1 d 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 20 of gross revenue What happens to the profit maximizing number of golf carts Please show all work and round to two decimal places when needed uc K e Add the above changes and add the values as point B on your uc MPK graph f 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 2 g The Federal government knowing all about the financial pains encountered by state and local governments given the Great Recession decides to offer an investment tax credit equal to 30 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 1000 rounds of golf and you get a 30 rebate from Uncle Sam so the investment tax credit adjusted price of the golf cart is now 700 rounds of golf 1 30 x 1000 420 Please show all work again and round to two decimal places when needed uc K h Add the above changes and add the values as point C on your uc MPK graph i Draw a desired investment diagram completely labeled with all the shift variables noted next to the function in parentheses with signs or depicting the 3 initial equilibrium no tax or tax credit as point A simply draw a negatively sloped ID curve going through point A Label the initial real interest rate as r A 08 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 04 Be sure to include all of the shift variables in parentheses next to this initial ID function j Then show as point B the new level of desired investment after the tax at the same real rate 08 Label this new level of desired investment as IdB again we don t have specific numbers for IdB Be sure to include all of the shift variables in parentheses next to your new ID function k 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 4 6 in the textbook 4 Finally 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 l 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 keep the economy from overheating 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 r 2 Explain how an increase in the real interest rate r would influence the uc MPK f diagram and how it would influence the desired investment Id diagram 5 3 A closed economy has full employment level of output Y of 7000 we got this from chapter 3 the interaction of labor supply and demand Government purchases G are 1600 taxes T are 1600 G and T are our exogenous variables Desired consumption Cd and investment Id are Cd 3200 0 2 Y T 2000r a Id 1200 3000r Solve for the desired savings function in intercept slope form note the intercept is an integer Sd b Name all the shift variables that are implicitly in the intercept of your savings function along with whether they share a positive or negative relationship with desired savings c Now solve for the goods market clearing interest rate Please show all work Id S d r 6 d Draw a desired savings investment diagram locating this initial equilibrium and point A e We know that GDP Y is comprised of C I G given our closed economy assumption Calculate the level of C I and G respectively along with the percent of each relative to GDP C C s of GDP I I s of GDP G G s of GDP 7 f We now consider expansionary fiscal policy as in an increase in G In particular G rises from 1600 to 2000 We are assuming the government spending multiplier is zero so that GDP is unaffected and remains at 7000 Resolve for the new market clearing interest rate and the associated levels of savings and investment Id S d r g Add this development to your diagram and label as point B h What has happened to the level of desired investment and why 8 i Support your argument by drawing a user cost MPK f diagram showing the movement from A to B j This phenomenon is referred to as k What has happened to the level of desired consumption and why Be specific and be sure to refer to the substitution effect in your answer 9