11DIFFERENTIATION - Department of Mathematics

FIGURE 11.12
The revenue is increasing on an interval
where the demand is inelastic, decreasing
on an interval where the demand is elastic,
and stationary at the point where the demand
is unitary.
EXAMPLE 8
SOLUTION ✔
S ELF-CHECK E XERCISES 11.4
y
Demand
is
inelastic.
Demand
is
elastic.
E(p) = 1
E(p) < 1 E(p) > 1
11.4 MARGINAL FUNCTIONS IN ECONOMICS 745
y = R(p)
REMARK As an aid to remembering this, note the following:
1. If demand is elastic, then the change in revenue and the change in the unit
price move in opposite directions.
2. If demand is inelastic, then they move in the same direction.
Refer to Example 7.
a. Is demand elastic, unitary, or inelastic when p 100? When p 300?
b. If the price is $100, will raising the unit price slightly cause the revenue to
increase or decrease?
a. From the results of Example 7, we see that E(100) 1 and E(300)
3 1. We conclude accordingly that demand is inelastic when p 100 and
elastic when p 300.
b. Since demand is inelastic when p 100, raising the unit price slightly will
cause the revenue to increase.
1. The weekly demand for Pulsar VCRs (videocassette recorders) is given by the
demand equation
p 0.02x 300 (0 x 15,000)
where p denotes the wholesale unit price in dollars and x denotes the quantity
demanded. The weekly total cost function associated with manufacturing these
VCRs is
C(x) 0.000003x 3 0.04x 2 200x 70,000 dollars
a. Find the revenue function R and the profit function P.
b. Find the marginal cost function C, the marginal revenue function R, and the
marginal profit function P.
c. Find the marginal average cost function C.
d. Compute C(3000), R(3000), and P(3000) and interpret your results.
2. Refer to the preceding exercise. Determine whether the demand is elastic, unitary,
or inelastic when p 100 and when p 200.
Solutions to Self-CheckExercises 11.4 can be found on page 749.
p