Question

The demand for a certain commodity isD(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? |

Answer #1

The demand for a certain product is Q(x,y) = 200 −
5x2 + 13xy units per month, where x is the price of the
product and y is the price of a competing product. It is estimated
that t months from now, the price of the product will be x(t)= 10 +
0.3t dollars per unit while the price of the competing product will
be y(t) = 12.8 + 0.2t2 dollars per unit. At what rate
will the demand for...

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?

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...

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

Market demand and supply for a commodity are given by the
following equations:
Demand: X = 30 – (1/3) P Supply: X = -2.5 + (1/2) P where X=
quantity (units), and P=price per unit ($)
Suppose that the government is planning to impose a tax on this
commodity and considering the following two options:
Option 1: A unit tax of $15
Option 2: An ad valorem tax of 20
What is the excess burden of each option?

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...

1. Market demand and supply for a commodity are given by the
following equations:
Demand: X = 30 – (1/3) P
Supply: X = -2.5 + (1/2) P where X= quantity (units), and P=price
per unit ($)
Suppose that the government is planning to impose a tax on this
commodity and considering the following two options:
Option 1: A unit tax of $15
Option 2: An ad valorem tax of 20%
a) Find the tax incidence on buyers and producers,...

If the demand equation for a certain commodity is given by the
equation: 550p + q = 86,000 where p is the price per unit; at what
price is there unitary elasticity? Round your answer off to two
decimal places. p =_____________?

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?

D(x) is the price, in dollars per unit, that consumers are
willing to pay for x units of an item, and S(x) is the price, in
dollars per unit, that producers are willing to accept for x
units. Find (a) the equilibrium point, (b) the consumer
surplus at the equilibrium point, and (c) the producer surplus
at the equilibrium point. D(x)=2500-10x, S(x)=400+25x

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