Question

Suppose the demand model and the cost function facing
a firm is expressed as

P= 120-5Q and

TC= 20+ 30Q + 2Q^{2}

1. Calculate

i. the
profit maximizing equilibrium level of output that the monopolist
will produce

ii. the
price that the monopolist would charge

iii. and
the profit of the monopolist

Answer #1

Q1. A monopolist has the following
demand function and marginal cost function P = 120 – Q and MC = 30
+ Q.
i. Derive the monopolist’s marginal revenue function.
ii. Calculate the output the monopolist should produce to
maximize its profit.
ii. (continuation)
iii. What price does the monopolist charge to maximize its
profit?
Now assume that the monopolist above split into two large firms
(Firm A and Firm B) with the same marginal cost as the
monopolist.
Let...

Suppose that a monopolist's inverse demand curve can be
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P= 10,000 +100Q - 10Q2 The monopolist's total cost
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a. Use Calculus to determine the monopolist's marginal revenue
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b. Use calcuus to determine the monopolist's marginal cost
curve
c. What is monopolist's profit-maximizing level of output?
d. What price should the monopolist charge to maximize its
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e. What is the profit that the monopolist makes?

A monopolist has a cost function given by C(Q)=Q2 and
faces the demand curve p=120-q
a. what is the profit maximizing monopolist output and price
b. what is the consumer surplus ? Monopoly profit?
c. now suppose the monopolist has to follow the narginal cost
pricing policy in other word she has to charge competitive prices
what is her output and price?

Suppose the demand function is given by P = 100-0. 02Q , and
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a fully labelled diagram. [5]

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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...

Consider two firms with the cost function TC(q) = 5q (constant
average and marginal cost,of 5), facing the market demand curve Q =
53 – p (where Q is the total of the firms’ quantities, and p is
market price).
a. What will be each firm’s output and profit if they make their
quantity choices simultaneously (as Cournot duopolists)?
b. Now suppose Firm 1 is the Stackelberg leader (its decision is
observed by Firm 2 prior to that firm’s decision)....

Given the Inverse Demand function as P = 1000-(Q1+Q2) and Cost
Function of firms as Ci(Qi) = 4Qi calculate the following
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A. In a Cournot Oligopoly (PC, QC, πC)
i. Find the Price (Pc) in the market,
ii. Find the profit maximizing output (Qi*) and
iii. Find the Profit (πiC) of each firm.
B. In a Stackelberg Oligopoly (PS, QS, πS),
i. Find the Price (PS) in the market,
ii. Find the profit maximizing output of the Leader (QL*)...

Consider a total cost function of TC = 0.5Q^2 +10Q + 20 and the
market demand function Q=70-p.
a What is the profit-maximizing output and price for the perfect
competition? Calculate its profit.
b What is the profit-maximizing output and price for the
monopolist? Calculate its profit.
c What is the profit-maximizing output and price for the
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a) Assume the firm operates in the monopoly market in the long
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showing the total cost of production, Q and P respectively of
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publish
i) Total revenue function (TR)
ii) Marginal revenue (MR)
iii) Marginal cost function (MC)
iv) Determine the level of price and quantity of production that
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v) Determine the amount of...

A monopolist facing a market demand Q = 240 – 2p has the total
cost function TC(q) = q2. Draw carefully the relevant
graph with MC, MR, D curves and identify all relevant points,
intersections, intercepts.
(a) What is the monopolist’s profit maximizing quantity and
price?
(b) If the market is reorganized as perfectly competitive, what
should be the market price and quantity?
(c) Calculate the DWL associated with the monopoly in (a).
Now the government notices that the monopolist...

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