Question

1. Consider a market with inverse demand P (Q) = 100 Q. A monopolist with linear cost C(Q) = 20Q serves this market.

(a) Find the monopolistís optimal price and quantity.

(b) Find the price, quantity, proÖt, consumer surplus, and social welfare under perfect competition.

(c) Find the optimal proÖt, consumer surplus, social welfare and the deadweight loss for monopoly.

(d) What is the % loss in social welfare as we move from perfect competition to monopoly.

Answer #1

1. Consider a market with inverse demand P (Q) = 100 Q and two
firms with cost function C(q) = 20q.
(A) Find the Stackelberg equilibrium outputs, price and total
profits (with firm 1 as the leader).
(B) Compare total profits, consumer surplus and social welfare
under Stackelberg and Cournot (just say which is bigger).
(C) Are the comparisons intuitively expected?
2. Consider the infinite repetition of the n-firm Bertrand game.
Find the set of discount factors for which full...

Inverse Demand Equation: P=160–4Qd Marginal Revenue =
160-8Qd Marginal Costs = $0
What is price and quantity under perfect
competition?
What price would a monopoly charge? How much will it
produce?
What is the deadweight loss due to
monopoly?
If the monopolist can practice perfect price
discrimination what is consumer surplus? What is producer
surplus?

The demand a monopolist faces is D(p) = 200 0
0.5p and the fifirm’s total cost is
c(q) =
150 + 20q.
1. Compute the profifit maximizing price and quantity, assuming
that the monopolist charges
a uniform price.
2. Draw a graph that illustrates the monopolist’s problem and
mark on it the consumer
surplus and the deadweight loss.
3. Compute consumer’s surplus, monopolist’s profifits and the
deadweight loss at the monopoly
price.

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.

6. Curse Purge Plus is a monopolist in the curse removal market
They face an inverse demand curve given by P=200-4Q, where Q is the
number of curse removals they sell. Their cost function is
C(Q)=10+8Q.
a. Write down the company’s profit function
b. Find the first-order condition for profit maximization.
c. Find the profit-maximizing price and quantity, and the
maximum profit.
d. Calculate the consumer surplus in the market at the monopoly
price and quantity.
e. If price were...

A monopolist faces inverse demand p = 40 − 2q and has a marginal
cost of 20.
(a) [20 points] What output will the monopolist produce?
(b) [10 points] What are consumer surplus, monopoly profits, and
deadweight loss?
(c) [10 points] Suppose the monopolist’s costs rise to 90. What
are consumer surplus, monopoly profits, and deadweight loss
now?
Please help to explain part (c).

A monopolist faces an inverse demand curve P(Q)= 115-4Q and
cost curve of C(Q)=Q2-5Q+100.
Calculate industry output, price, consumer surplus, industry
profits, and producer surplus if this firm operated as a
competitive firm and sets price equal to marginal cost.
Calculate the dead weight loss sue to monopoly.

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

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.

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