Desired Capital, User Cost and Goods Market Equilibrium

Instructions: Please show all work or points will be taken off. Good luck!

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 400 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 = 420 – 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*)?

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

A completely labeled and correct graph is worth 10 points.

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 so-called “luxury tax” (we know it as τ) equal to 20% 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 15% (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 = 400 rounds of golf) and you get a 15% rebate from Uncle Sam so the investment tax credit adjusted price of the golf cart is now 340 rounds of golf [(1-.15) x 400 = 340]. Please show all work again and label this as point C on your uc/MPK diagram.