08 Jun Question Economics 304– Homework – Lesson 5 – Th
Question
Economics 304– 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
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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) 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.
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* = 1 c) Draw a graph (the uc / MPK graph) depicting the state of affairs and label this initial profit maximizing point as point A. 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* = 2 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!) ……………..” 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 = 700].
Please show all work again and round to two decimal places when needed. uc = K* = 3 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
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 = .08.
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
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