For a Monopolist, the inverse demand function is P=80 – Q (Or,
the Demand function is...
For a Monopolist, the inverse demand function is P=80 – Q (Or,
the Demand function is Q = 80 – P, if you prefer). The firm’s total
cost function is 20 + 5Q + .5Q2.
Identify profit maximizing quantity and price Q =
_____, P = _____
Graph the relevant curves in the area provided (Hint: If you
have difficulty drawing the graph, try plotting a couple of points
along the curve)
Identify CS and PS in the graph Calculate CS and PS: CS =
________ PS = ___________
Calculate elasticity of demand at the profit maximizing
price
A monopolist faces the inverse demand for its output: p = 30 −
Q. The monopolist also has a constant marginal and average cost of
$4/unit.
(a) (10 points) What is the monopolist’s profit-maximizing level
of output? What is the monopolist’s profit at this level of
output?
(b) (10 points) Calculate the consumer surplus and show it in a
graph along with the monopolist’s equilibrium; label the
monopolist’s equilibrium e M.
(c) (2.5 points) What would the competitive equilibrium be...
Acme is a monopolist who faces inverse market demand function P
(Q, y) = 100 - 2Q + y, where y is the quality level of Acme’s
product. Acme has cost function function C(Q) = 20Q.
Suppose quality is costly. Specifically, assume that Acme must
pay innovation cost I(y)= (1/4)(y^2). Thus, Acme’s total profits
are x(Q,y)=P(Q,y)Q - C(Q) - I(y). Assuming Acme is allowed to act
like a monopolist, we will work out Acme’s optimal quality choice,
y*.
1. Suppose,...
Monopoly with linear inverse demand. Consider a monopolist
facing a linear inverse demand curve p(q)= a- bq, and cost function
C(q)= F + cq, where F denotes its fixed costs and c represents the
monopolist's (constant) magical cost a>c
1. Graph demand, marginal revenue and marginal cost. Label your
graph carefully, including intercepts
2. Solve the profit maximizing output q^m. To do this, first
write down the expression for MR=MC and solve for the optimal
quantity. Next find the price...
A monopolist serves market A with an inverse demand curve of P =
12 – Q. The marginal cost is constant at $2. Suppose the monopolist
uses a two-part tariff pricing. What price does the monopolist set?
What is the entrance fee? What is the deadweight loss? What is
consumer surplus?
A monopolist sells in a market described by the inverse demand
function p = 10 - 0.1Q , where p is the price and Q is the
total quantity sold. The monopolist produce its output in two
plants which have the cost functions C 1 = 0.25q 1 and C
2 = 0.5q 2 , where q i (i=1,2) is the output produced
in plant i (of course,...
The market (inverse) demand function for a homogenous good is
P(Q) =
10 – Q. There are three firms: firm 1 and 2 each have a total cost
of Ci(qi) = 4qi for i ∈ {1.2}. and firm 3 has a total cost of
C3(q3) = 2q3. The three firms compete by setting their quantities
of production, and the price of the good is determined by a market
demand function given the total quantity. Calculate the Nash
equilibrium in this...
A monopolist faces a market demand: P = 200 – Q. The monopolist
has cost function as C = 1000 + Q2, and marginal cost MC = 2Q.
(
1) Solve for Marginal Revenue (MR) function.
(2) Find the profit-maximizing quantity? Profit?
(3) Suppose the monopolist decides to practice 3rd degree price
discrimination. Without solving for the 3rd degree price
discrimination, can you compare the new profit earned by the
monopolist with the old profit?
A monopolist faces a market (inverse) demand curve P = 50 − Q .
Its total cost is C = 100 + 10Q + Q2 .
a. (1 point) What is the competitive equilibrium benchmark in
this market? What profit does the firm earn if it produces at this
point?
b. (2 points) What is the monopoly equilibrium price and
quantity? What profit does the firm earn if it produces at this
point?
c. (2 points) What is the deadweight...
A monopoly has an inverse demand function given by p = 120 - Q
and a constant marginal cost of 10. a) Graph the demand, marginal
revenue, and marginal cost curves. b) Calculate the deadweight loss
and indicate the area of the deadweight loss on the graph. c) If
this monopolist were to practice perfect price discrimination, what
would be the quantity produced? d) Calculate consumer surplus,
producer surplus, and deadweight loss for this monopolist under
perfect price discrimination.
A monopolist with the cost function C(q) = q faces the
market demand curve
p = 101 -2q. What is the maximum amount the monopolist is
willing to pay for advertising that shifts its demand curve to
p = 101-q?