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*)?
c) Draw a graph (the uc / MPK graph) depicting the state of affairs and label this initial profit maximizing point as point A.
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 socalled “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 againand 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 of the shift variables in parentheses next to this initial ID function.
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 of the shift variables in parentheses next to your new ID function
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.
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) 600r
Id= 600 400r
a) 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.
We now have a change in the desired investment function – it is now:
Id= 570 400r
c) 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.
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.