ECON304 HW5

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Pennsylvania State University, World Campus *

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Economics

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Jan 9, 2024

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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
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
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