Question

**Suppose the cost of producing q unit is
c(q)=500-4q+q2 and the
demand function is given by p=14-2q**

A) Develop the total revenue, total cost (if not given), and profit functions. Explain these functions in few sentences.

B) Compute the point elasticity of demand.

C) Find the intervals where the demand is inelastic, elastic, and the price for which the demand is unit elastic.

D) Find the quantity that maximizes the total revenue and the corresponding price. Interpret your result.

E) Find the quantity that minimizes the average cost function and the corresponding price. Interpret your results.

F) What are the quantity and the price that maximize the profit? What is the maximum profit? Interpret your result.

G) **Discuss the results of D, E and F.**

Answer #1

The demand function for a monopolist's product is
p=1300-7q and the average cost per unit for producing q
units is
c=0.004q2-1.6q+100+5000/q
-Find the quantity that minimizes the average cost function and
the corresponding price. Interpret your results.
-What are the quantity and the price that maximize the profit?
What is the maximum profit? Interpret your result.

Consider a firm with the demand function P(Q)=(50-2Q), and the
total cost function TC(Q)=10,000+10Q. Find the profit maximizing
quantity. Calculate the profit maximizing price (or the market
price). Hint: MR(Q)=(50-4Q),

Your hospital has a demand function given by P = 404 - 2Q where
P is the price of hospital care and Q is the quantity of hospital
care. The marginal revenue (MR) function is given by MR = 404 – 4Q.
The total cost function (TC) is given by TC = 300 + 4Q +
8Q2 and the marginal cost (MC) is given by MC = 4 +
16Q.
Find the total revenue (TR) function which is a function...

The Pampered Pig, purveyors of premium pork products, estimate
that the total cost of producing ?q pounds of their Premier Pork
Packed Potatoes is estimated by the function
C(q) = q^2 + 4q + 100
and
p(q) = 100 - 2q
is the price at which all units of their premier pork packed
potatoes will be sold.
a. Find the revenue function.
b. Find the profit function.
c. Find the marginal revenue function.
d. Find the marginal cost function.
e....

The demand for product Q is given by Q = 136 -.4P and
the total cost of Q by:
STC = 3000 + 40Q - 5Q^2 + 1/3Q^3
A. Find the price function and then the TR function. See
Assignment 3 or 4 for an example.
B. Write the MR and MC functions below. Remember: MR =
dTR/dQ and MC = dSTC/dQ. See Assignment 5 for a review of
derivatives.
C.What positive value of Q will maximize total
profit? Remember, letting...

2. Suppose the demand function for a monopolist’s product is
given by: Q = 80 – 5P (Total marks = 5) and the cost function is
given by C = 30 + 2Q + 0.5Q2 A) What is the inverse demand function
for this monopoly? B) Calculate the MC. C) Calculate the MR. D)
Determine the profit-maximizing price. E) Determine the
profit-maximizing quantity. F) How much profit will the monopolist
make? G) What is the value of the consumer surplus...

the
demand equiation of a goof is given by P+2Q=20 abd the total cost
function is Q3-8Q^2+20Q+2
a) find the level of output that maximizes total revenue
b) find the maximum profit and the value of Q at which it is
achieved. verify that, at this value of Q, MR=MC

1) The inverse demand curve a monopoly faces
is
p=110−2Q.
The firm's cost curve is
C(Q)=30+6Q.
What is the profit-maximizing solution?
2) The inverse demand curve a monopoly faces
is
p=10Q-1/2
The firm's cost curve is
C(Q)=5Q.
What is the profit-maximizing solution?
3) Suppose that the inverse demand function for
a monopolist's product is
p = 7 - Q/20
Its cost function is
C = 8 + 14Q - 4Q2 + 2Q3/3
Marginal revenue equals marginal cost when output
equals...

The demand function for a Christmas music CD is given by
q=D(p)=0.25(225−p2)where q (measured in units of a hundred) is the
quantity demanded per week and p is the unit price in dollars. (a)
Find the elasticity function E(p)= _________
(b) Evaluate the elasticity at 10. E(10)= ________
(c) Should the unit price be lowered slightly from 10 in order
to increase revenue? Yes or No.
(d) Use the elasticity of demand to find the price which
maximizes revenue for...

the demand function P=1600-4q is for trucks (p=price
q=quantity)
Average cost= (300/q)+20
is my TC=300+20q since TC=AC*Q
Q- How many trucks must be produced and sold to maximise total
profit ?

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