Question

1. In this problem, *p* and *C* are in dollars and
*x* is the number of units.

A monopoly has a total cost function

*C* = 1000 + 216*x* + 0*x*^{2} for
its product, which has demand function *p* = 648 ?
3*x* ? 2*x*^{2}.

Find the consumer's surplus at the point where the monopoly has maximum profit. (Round your answer to the nearest cent.)

2. In this problem, *p* is in dollars and *x* is
the number of units.

Suppose that the supply function for a good is *p* =
4*x*^{2} + 10*x* + 5.

If the equilibrium price is $341 per unit, what is the producer's surplus there? (Round your answer to the nearest cent.)

3. In this problem, *p* is in dollars and *x* is
the number of units.

If the supply function for a commodity is *p* =
10*e*^{x/3},

what is the producer's surplus when 15 units are sold? (Round your answer to the nearest cent.)

4. In this problem, *p* is in dollars and *x* is
the number of units.

Find the producer's surplus at market equilibrium for a product if
its demand function is *p* = 100 ?
*x*^{2}

and its supply function is *p* = *x*^{2} +
8*x* + 58.

(Round your answer to the nearest cent.)

Answer #1

In this problem, p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if
its demand function is p = 100 − x2 and its supply function is p =
x2 + 6x + 44. (Round your answer to the nearest cent.)

In this problem, p, price, is in dollars and x
is the number of units.
The demand function for a product is
p = 206 − x2.
If the equilibrium price is $10 per unit, what is the consumer's
surplus? (Round your answer to two decimal places.)
In this problem, p is in dollars and x is the
number of units.
The demand function for a certain product is
p = 81 − x2 and
the supply function is p...

The demand for a particular item is given by the demand
function
1. D(x)=200−x^2
Find the consumer's surplus if the equilibrium point
(Xe,Pe)=(5,175) Round to the nearest cent.
$____
2. The demand for a particular item is given by the function
D(x)=1,350−3x^2. Find the consumer's surplus if the equilibrium
price of a unit $150
The consumer's surplus is $___
3. The demand for a particular item is given by the function
D(x)=120/x+6. Find the consumer's surplus if the equilibrium price...

3. Solve the following problem: The supply function for x units
of a commodity is p = 30 + 100 ln ( 2 x + 1 )dollars and the
demand function is p = 700 − e^0.1x. Find both the consumer's and
producer's surpluses. Use your graphing calculator to find the
market equilibrium and compute definite integrals necessary to
compute the surpluses. Note you won't be able to do some of the
integrals otherwise. Explain your steps.
4. Sketch...

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 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.)

22. Consumers' and Producers' Surplus. The quantity demanded
x (in units of a hundred) of the Sportsman 5 ✕ 7 tents,
per week, is related to the unit price p (in dollars) by
the relation
p = −0.1x2 − x + 50.
The quantity x (in units of a hundred) that the
supplier is willing to make available in the market is related to
the unit price by the relation
p = 0.1x2 + 4x + 20.
If the market...

In this problem, p is the price per unit in dollars and q is the
number of units. If the weekly demand function is p = 120 − q and
the supply function before taxation is p = 12 + 5q, what tax per
item will maximize the total revenue?

In this problem, p is the price per unit in dollars and
q is the number of units.
If the weekly demand function is
p = 120 − q
and the supply function before taxation is
p = 8 + 6q,
what tax per item will maximize the total revenue?
$____ /item

1). Find the consumer and producer surpluses by using the demand
and supply functions, where p is the price (in dollars)
and x is the number of units (in millions).
Demand Function
Supply Function
p = 410 − x
p = 160 + x
consumer surplus $_________
millionsproducer surplus $ ________millions
2) Find the consumer and producer surpluses by using the demand
and supply functions, where p is the price (in dollars)
and x is the number of units (in...

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