(Problem 1: 25)
Economics: Demand for DVD Rentals. Klix Video has found that demand for
rentals of its DVDs is given by q = D(x) = 140 - 40x,
where q is the number of DVDs rented per day at x dollars per rental. Find each of the
following.
a. The quantity demanded when the price is $2 per rental
b. The elasticity as a function of x
c. The elasticity at x=2 and x= 5 at Interpret the meaning of these values of the elasticity.
d. The value of E(x=1) for which Interpret the meaning of this price.
e. The total-revenue function, R(x)= x.D(x)
f. The price x at which total revenue is a maximum
(Problem 2: 25)
Given ln 5 = 1.6094 and ln 2 = 0.6931, find each of the following:
a) ln 10 b) ln 2/5 c) ln 5/2 d) ln 32 e) ln 5e2
ln 5.2=ln 5+ln 2=1.6094+0.6931
ln 2/5=ln 2-ln 5=0.6931-1.6094
ln 5/2=ln 5-ln 2=1.6094-0.6931
ln 32=ln (2^5)=5.ln 2=5*(0.6931)=
ln 5e^2=ln5+lne^2=1.6094+2*ln e=1.6094+2*(1)=3,6094
(Problem 3: 25)
Following the birth of their granddaughter, two grandparents want to make an initial investment
of that will grow to $10,000 by the child’s 20th birthday. What should the initial investment be?
If Interest is compounded :
a. Continuously at 6%.
b. Annually at 6%
c. Semi-annually at 6%
d. Quarterly at 6%
(Problem 4: 25) Big Tree McGee is negotiating his rookie contract with a professional basketball
team. They have agreed to a three-year deal which will pay Big Tree a fixed amount
at the end of each of the three years, plus a signing bonus at the beginning of his first year. They
are still haggling about the amounts and Big Tree must decide between a big signing bonus and
fixed payments per year, or a smaller bonus with payments increasing each year. The
two options are summarized in the table. All values are payments in millions of dollars.
Signing bonus Year 1 Year 2 Year 3
Option #1 6.0 2.0 2.0 2.0
Option #2 1.0 2.0 4.0 6.0
(a) Big Tree decides to invest all income in stock funds which he expects to grow at a rate of 10%
per year, compounded continuously. He would like to choose the contract option which gives
him the greater future value at the end of the three years when the last payment is made. Which
option should he choose?
(b) Calculate the present value of each contract offer.