Economics 100 – Key for Problem Set #4
Spring 2007
Page 1 of 4
1.
The builder of a new movie theater complex is trying to decide how many screens she wants.
The cost of construction is $1,000,000 per screen.
The builder is borrowing from the bank at
some real interest rate to build the movie theater complex.
Listed below are the number of
patrons the complex will attract, depending on the number of screens (6 points):
Number of Screens
Total Number of
Patrons per year
Increase in Patrons
for each Screen
Marginal Revenue of
each Screen
1
40,000
40,000
$80,000
2
75,000
35,000
$70,000
3
105,000
30,000
$60,000
4
130,000
25,000
$50,000
5
150,000
20,000
$40,000
a.
Suppose that after paying the movie distributor and all other noninterest expenses the owner
expects to net $2.00 per ticket sold.
The increase in patrons for each screen is the change in
the total number of patrons per year.
The marginal revenue for each screen is the increase in
patrons for each screen (number of tickets) times $2.00 per ticket.
b.
If the bank is charging a real interest rate (
R
) of 0.045, then the marginal cost of borrowing
to pay for each screen is $45,000.
Using the profit-maximizing rule that a firm invests so
long as the marginal revenue
≥
marginal cost, the builder will build
4 screens
.
c.
If the bank is charging a real interest rate (
R
) of 0.055, then the marginal cost of borrowing
to pay for each screen is $55,000.
Using the profit-maximizing rule that a firm invests so
long as the marginal revenue
≥
marginal cost, the builder will build
3 screens
.