ECON304 HW5

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Economics 304WD -- Homework - Lesson 5 – The Desired Capital stock, Investment Demand, and Goods Market Equilibrium – 120 Points (5 points each part)  You need to show your work, not just the final answer  Use the template to complete your work or points will be taken off.  Please put your name and PSU ID number at the top of the page  Save the file on your computer ( .PDF is the only format allowed ) and then upload it to the Canvas dropbox for this homework assignment.  Be sure your assignment is all on one file. Failure to submit a single file will result in points being deducted 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 in- formation 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 MPK f = 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 ini- tial profit maximizing point as point A . 260 74 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 τ) equal to 15% of gross revenue What happens to the profit maximizing number of golf carts? Please show all work and round to two decimal places. 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 us- ing 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!) ……………..” 69.412 305.882 If I did not change my capital input, then I would not be meeting the circumstances of profit maximization. UC will be greater than MPKf to have UC=MPKf, we need to decrease K*. 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 invest- ment 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 in- vestment 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 = 2000 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 1400 rounds of golf [(1-.30) x 2000 = 1400]. Please show all work again . uc = K* = h) Add the above changes and add the values as point C on your uc/MPK graph. 78.588 214.117 3

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i) Draw a desired investment diagram (completely labeled with all the shift vari- ables noted next to the function in parentheses with signs (+ or -)) depicting the initial equilibrium (no tax or tax credit) as point A (simply draw a negatively sloped I D 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 I d A . Note im- portantly 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 = .08. Be sure to include all of the shift variables in parentheses next to this initial I D 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 I d B (again, we don’t have specific numbers for I d B . Be sure to include all of the shift variables in parentheses next to your new I D function k) Why did the level of desired investment change, even though the real rate of in- terest did not? Please be specific using the equation that connects the desired capi- tal stock (K*) to desired investment. (4.6 in the textbook). The desired investment level changed because the desired investment is inversely dependent on the tax rate. Since the tax rate increased, the desired investment decreased, leading to K*. 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 I d C (again, we don’t have specific numbers for I d C ). Make sure you include all of shift variables in parentheses next to your new I D 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 Govern- ment), what would they have to do to the real rate of interest to achieve their ob- jective? 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 dia- gram and how it would influence the desired investment (I d ) diagram. When r increases, UC increases, and K* declines. The MPK line remains constant. UC changes the motion following the MPK curve on the I diagram. When r increases, the change moves along. 10.79% 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 1680, taxes (T) are 1600 (G and T are our exogenous variables). Desired con- sumption (C d ) and investment (I d ) are: C d = 3200 + 0.2( Y –T) - 2000 r I d = 1200 - 3000 r a) Solve for the desired savings function in intercept - slope form (note, the inter- cept is an integer). S d = 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 de- sired savings. c) Now solve for the goods market clearing interest rate. Please show all work. 2000r-1120 [+] Y. [-] g [-] Yf [-] A [-] cc [-] Af [+] t 1152 1.6% 6

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I d = S d = r = 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 as- sumption. 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 = 60.61 % 4248 16.46% 1152 22.86% 1600 7

f) We now consider expansionary fiscal policy as in an increase in G. In particular, G rises from 1680 to 2000. We are assuming the government spending multiplier is zero so that GDP is unaffected and remains at 7000. Resolve for the new mar- ket clearing interest rate and the associated levels of savings and investment. I d = 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! Crowding out When r increases, the consumpution level declines. The substitution effect is when consumers substitute future consumption with present consumption 9

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