Question

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 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.
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.​
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.

Answer 1

a) 260 rounds of golf

b) 74

c) attached below

d) 70 golf carts

Step-by-step explanation:

a) Calculate the user cost of capital and what is it expressed in

user cost of capital = total depreciation + total interest

= ( rate of depreciation * Golf cart cost ) + ( real interest rate * Golf cart cost )

= ( d + r ) Golf cart cost

= ( 0.05 + 0.08 ) 2000 = 260 rounds of golf

b) determine the number of carts that should be bought to maximize profits

Profits are maximized when User Cost of capital = MPKF

(d +r) Golf cart cost = MP Kf = 1000 – 10K

( 0.05 + 0.08 ) 2000 = 1000 – 10K

260 = 1000 – 10K ∴ K = ( 1000 - 260 ) / 10 = 74

c) attached below is the required graph

d) Determine what happens to the profit maximizing number of golf carts

User cost of capital ( 1 - t ) = MPK^f

∴ User cost of capital ( 1 - t ) = 1000 – 10K

260 ( 1 - 0.15 ) = 1000 – 10K

305.88 = 1000 – 10K

K=69.41

that is approximately 70 golf carts is been bought to maximize profit