You own a golf resort 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. Please be sure to SHOW all work!

A brand new golf cart costs 300 rounds of golf (this is your output) and the rate of depreciation is 3% (0.03).

The real interest rate is 7% (.07).

And the expected marginal product of capital is given by MPK^f=300 - 2K.

There is a tax on capital so tao () = 25% (.25)

a)(10 points) What is the (tax adjusted) user cost of capital and what is this user cost expressed in? (Show work)

b) (5 points) How many golf carts should you buy to maximize profits? Show work

Draw a uc/K graph depicting the state of affairs and label this initial profit maximizing condition as point A.

A correctly drawn and completely labeled diagram is worth 20 points

Now conditions change.The following two shocks occur simultaneously:

i)due to supply bottlenecks the price of golf carts rises to 360 rounds of golf.

ii) the expected marginal product of capital changes and is now MPK^f= 280 - 2K.

c) (5 points) Resolve for K* and show as point B on your uc/K diagram.

d) (10 points) Given the two shocks as above, explain the intuition underlying the change in the profit maximizing level of carts (i.e., why does the firm change its behavior?), making sure you refer to the firm's profit maximizing condition (write it out!).Be specific and write this like you were a professional economist! Be sure to compare the actual user cost to the actual MPK^f after the shocks, holding K constant at its level from part b).

e) (10 points) Suppose that the Federal Reserve had a goal to get the capital stock, the number of golf carts purchased to equal 48. Given the two shocks as above, 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 = ?). Please add this development to BOTH OF YOUR DIAGRAMS and label point C.

f) Finally, draw a desired investment diagram (completely labeled with the ALL the shift variables) depicting the initial equilibrium as point A (simply draw a negatively sloped I^D curve going through point A).Label the initial level of desired investment as I^d_A. Note importantly that we do not have numbers for desired investment, but that's ok, we are focusing on the change in desired investment. Then show, as point B, after the two shocks. Finally, show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as I^d_C.

A completely labeled and correct diagram is worth 20 points (make sure you include ALL the shift variables in parentheses or points will be taken off).