Question

If, in a monopoly market, the demand function for a product is p = 145 − 0.80x and the revenue function is R = px, where x is the number of units sold and p is the price per unit, what price will maximize revenue?

Answer #1

If, in a monopoly market, the demand for a product is p
= 120 − 0.80x and the revenue function is R =
px, where x is the number of units sold, what
price will maximize revenue? (Round your answer to the nearest
cent.)

The demand function for a particular brand of LCD TV is given
by
p = 2400 − 30x
where p is the price per unit in dollars when
x television sets are sold.
(a) Find the revenue function.
R(x) =
(b) Determine the number of sets that must be sold in order to
maximize the revenue.
sets
(c) What is the maximum revenue?
$
(d) What is the price per unit when the revenue is maximized?
$ per unit

The monthly demand function for x units of a product
sold by a monopoly is
p = 6,100 −
1/2x2 and its average cost
is C = 3,030 + 2x dollars. Production is
limited to 100 units.
a) Find the profit function, P(x), in dollars.
b) Find the number of units that maximizes profits. (Round your
answer to the nearest whole number.)
c) Find the maximum profit. (Round your answer to the nearest
cent.)

The short term demand for a product can be approximated by q =
D(p) = 18 − 2 √p where p represents the price of the product, in
dollars per unit, and q is the number of units demanded. Determine
the elasticity function. Use the elasticity of demand to determine
if the current price of $50 should be raised or lowered to maximize
total revenue.

The monthly demand function for a product sold by a monopoly is
p = 2200 − (1/3)x^2 dollars, and the average cost is C = 1000 + 10x
+ x^2 dollars. Production is limited to 1000 units and x is in
hundreds of units.
(a) Find the quantity (in hundreds of units) that will give
maximum profit.
(b) Find the maximum profit. (Round your answer to the nearest
cent.)

Suppose that the price p (in dollars) of a product is given by
the demand function p = (18,000 − 60x) / (400 − x) where x
represents the quantity demanded and x < 300. f the daily demand
is decreasing at a rate of 100 units per day, at what rate (in
dollars per day) is the price changing when the price per unit is
$30?

The weekly demand function for x units of a product
sold by only one firm is p = 400 − 1/2x dollars, and the average
cost of production and sale is
C = 100 + 2x dollars.
(a) Find the quantity that will maximize profit.
units
(b) Find the selling price at this optimal quantity.
$ per unit
(c) What is the maximum profit?
$
The weekly demand function for x units of a product sold by only
one firm is...

3. As the number of units sold increases, market price decreases
(supply and demand).
Suppose that p = 5000 – 0.75x , where p
is the market price and x is the number of
units sold. Suppose further that the
cost of producing x items is given by
C(x) = 3000 + 15x, and that the revenue
from the sale of x units is given by
R(x) = 120x.
a. Express the cost as a...

The demand function for a product is given by p=80-0.5Q and the
supply function is p=50+0.25Q, where p is the price and Q is the
quantity. Suppose that the government impose a tax of $15 on every
unit sold.
a) Find equilibrium price and quantity before imposing the
tax.
b) Find price of buyer and seller and the quantity sold in the
market after tax.
c) Find the tax burden on buyer and seller.
d) Find government revenue and deadweight...

The demand function for a certain product is p = 3000, where q
is the quantity of the product produced and q sold while p is the
unit price when q units are produced.
Find the point elasticity of demand when q = 300.
Is the demand elastic, inelastic, or unit elastic when q =
300?

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