Question

The price p (dollars per unit) of a particular commodity is increasing at the rate p ' (x) = (20/((x + 7)) with superscript (2)) , when x hundred units of the commodity are supplied to the market. The manufacturer supplies 300 units when the price is 3 $ per unit. What price corresponds to a supply of 1300 units?

Answer #1

The demand for a particular commodity when sold at a price of p
dollars is given by the function D(p) = 4000e −0.02p .
(a) Find the price elasticity of demand function and determine
the values of p for which the demand is elastic, inelastic, and of
unitary elasticity.
(b) If the price is increased by 3% from $12, what is the
approximate effect on demand?
(c) Find the revenue R(p) obtained by selling q units at p
dollars per...

The price of a certain commodity in dollars per unit at time
t (measured in weeks) is given by
p=8+4e^(-5t)+te^(-5t)
.
How fast is the price of the commodity changing at ?
a.
Increasing at the rate of $19/wk.
b.
Decreasing at the rate of $19/wk.
c.
Increasing at the rate of $11/wk.
d.
Decreasing at the rate of $11/wk.
e.
Increasing at the rate of $8/wk.
2.
Lynbrook West, an apartment complex, has 100 two-bedroom units.
The...

Suppose that the demand curve for a particular commodity is
P=17-2D, where D is the quantity demanded and P is the price. The
supply curve for the commodity is P=2+S, where S is quantity
supplied. (1)Find the equilibrium price and
output. Suppose now that a unit tax of 3 dollars is
imposed on the commodity. (2) Show the new equilibrium is
the same regardless of whether the tax is imposed on producers or
buyers of the commodity. (3) Calculate the...

p is the price per unit in dollars and q is the number of
units.
If the weekly demand function is p=200-2q^2 and the supply
function before taxation is p=20+3q, what tax per item will
maximize the total tax revenue?

The demand for a certain commodity is
D(x) =
8000e−.08x
units per month when the market price is x dollars per
unit.
(a)
At what rate is the consumer expenditure E(x)
= xD(x) changing with respect to price x
when the price is equal to $180 dollars?
(b)
At what price does consumer expenditure stop increasing and
begin to decrease?
(c)
At what price does the rate of consumer expenditure
begin to increase?

A manufacturer estimates that when q thousand units of a
particular commodity are produced each month, the total cost will
be C(q) =0.4q 2 +3q+40 thousand dollars, and all q units can be
sold at a price of p(q)= 22.2 - 1.2q dollars per unit. At what
level is the average cost per unit minimized?
a)10 thousand
b)17.6 thousand
c)9 thousand
d)6 thousand

In this problem, p is the price per unit in dollars and
q is the number of units.
If the demand and supply functions for a product are
p = 840 ? 2q and p = 100 +
0.5q,
respectively, find the tax per unit t that will
maximize the tax revenue T.

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?

In this problem, p is the price per unit in dollars and
q is the number of units.
If the demand and supply functions of a product are
p = 5000 − 20q −
0.7q2 and p = 500 +
10q + 0.3q2,
respectively, find the tax per unit t that will
maximize the tax revenue T.
T= $/Item

In this problem, p is the price per unit in dollars and q is the
number of units. If the demand and supply functions of a product
are p = 6500 − 5q − 0.7q2 and p = 500 + 10q + 0.3q2, respectively,
find the tax per unit t that will maximize the tax revenue T. t = $
/item

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