Question

Consider a market with demand given by P = a−bQ, where a,b > 0. Suppose the only supplier in the market has costs given by C(Q) = mQ+F, where ﬁxed cost is F > 0 and sunk and m is positive but small enough that the ﬁrm does not shut down.

(1) Find the monopolist’s proﬁt-maximizing price and quantity and the monopolist’s proﬁts.

(2) Show that the proﬁt-maximizing monopolist produces on the elastic portion of its demand curve (in the short run).

Answer #1

1)

P = a - bQ (Market demand curve)

Total revenue = PQ = (a-bQ)Q

Marginal revenue

MR =

Cost function C(Q) = mQ + F where F > 0 are the fixed costs

For the profit maximizing monopolist,

(Equilibrium quantity)

Equilibrium price is found from the inverse demand curve:

And monopolist's profits

2)

Inverse demand curve: P = a - bQ

Price elasticity of demand

From our inverse demand curve, we can find that

But

Thus proﬁt-maximizing monopolist produces on the elastic portion of its demand curve.

Consider a monopolist facing a market demand given by
P = 100 - 2Q
where P Is the price and Q is the quantity. The monopolist
produces the good according to the cost function
c(Q)=Q2+10
(a) Determine the profit maximizing quantity and price the
monopolist will offer in the market
(b) Calculate the profits for the monopolist.
(c) Calculate the deadweight loss due to a monopoly. Illustrate
this In a well labelled diagram.

Consider a monopolist facing a market demand given by
p=100-2q
Where p is the price and q is the quantity, the monopolist produces
good according to the cost function c(q)=q^2 +10
A determine the profit-maximizing quantity and the price the
monopolist will offer in the market
B calculate the profits for the monopolist
C calculate the deadweight loss due to a monopoly. Illustrate
this in a well-labelled diagram.

1. A monopolist operates in an industry where the demand curve
is given by Q = 1000 ? 2P. The monopolist’s has constant marginal
cost of $8 (and no fixed costs). What is the monopolist’s
profit-maximizing price? How much does the monopolist produce? What
are its profits?

Consider a monopolist facing a market demand given by:
P = 100 – 2Q
Where P is the price and Q is quantity. The monopolist produces
the good according to the cost function c(Q) = Q2 +
10.
Determine the profit-maximizing quantity and price the
monopolist will offer in the market
Calculate the profits for the monopolist
Calculate the deadweight loss due to a monopoly. Illustrate
this in a well labeled diagram.

Suppose a monopolist faces market demand (Dm) of P(q) = a - bq
and whose cost is C(q) = cq where c is a positive constant.
a. What the marginal revenue of the monopolist?
b. What is the monopoly price?
c. What is the monopolist's output at the price found in part
(b)?
d. What would be the market clearing price and quantity under
perfect competition

A patent monopolist faces a demand curve: P=10-1/3 Q and total
cost F+2Q+2/3 Q^2, where F is non-negative.
i. What is the monopolist’s short-run profit-maximizing output
and price? What is his short-run profit per period?
ii. In addition to solving for the profit-maximizing output and
price, draw a graph showing the inear demand curve, the marginal
revenue and marginal cost curves that demonstrate the situation
described above

A monopolist faces the demand for its product: p = a - bQ. The
monopolist has a marginal cost given by c and a fixed cost given by
F. Answer the following questions, while showing all of your
derivation steps. Just providing final answer does not warrant any
mark.
2-a) Assume that F is sufficiently small such that the
monopolist produces a strictly positive level of output. What are
the profit-maximizing price and quantity?
2-b) Compute the maximum profit for...

1. Consider a monopolist where the market demand curve
for the produce is given by P = 520 - 2Q. This monopolist has
marginal costs that can be expressed as MC = 100 + 2Q and total
costs that can be expressed as TC = 100Q + Q2 + 50. (Does not need
to be done. Only here for reference)
2. Suppose this monopolist from Problem #1 is regulated
(i.e. forced to behave like a perfect competition firm) and the...

A monopolistic firm produces goods in a market where the demand
function is P = 43 − 0.3Q and the corresponding total cost
function is TC=0.01Q^3-0.4Q^2+3Q
e) Calculate the price elasticity of demand at the profit
maximizing Q (use Q>0). Comment (elastic, inelastic or unit
elastic?) on the calculated price elasitity of demand. Is the good
is necssary or luxary?
f) What would happen to the revenue of the firm if price goes
down? [Use the vlaue of price...

Suppose a monopolist faces the following demand curve: P = 750 –
Q.If the long run marginal cost of production is constant and equal
to $30.
a) What is the monopolist’s profit maximizing level of
output?
b) What price will the profit maximizing monopolist charge?
c) How much profit will the monopolist make if she maximizes her
profit?
d) What would be the value of consumer surplus if the market
were perfectly
competitive?
e) What is the value of the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 23 minutes ago

asked 40 minutes ago

asked 40 minutes ago

asked 40 minutes ago

asked 52 minutes ago

asked 52 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago